Copy number variant caller

ABSTRACT

Direct targeted sequencing (DTS) methods and a hidden Markov model (HMV) can be used to call the copy number of a segment of interest within a region of interest. Described herein are methods for calling a copy number variant or a copy number variant abnormality using an HMM, and methods for determining a copy number based on a copy number likelihood model, in a test sequencing library that has be sequenced using DTS methods. Also described herein are methods for determining a copy number of a segment, including accounting for spurious capture probes that may arise from the DTS methods.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.15/934,839, filed Mar. 23, 2018, which claims priority benefit of U.S.Provisional Application No. 62/476,361, filed on Mar. 24, 2017, entitled“COPY NUMBER VARIANT CALLER,” the entire contents of which isincorporated herein by reference for all purposes.

TECHNICAL FIELD

The present invention relates to methods for determining a copy numberof a genetic region of interest.

BACKGROUND

There have been many important advances in the understanding of thehereditary susceptibility to cancer and other diseases. Identificationof mutations associated with hereditary cancer syndromes and otherdiseases can lead to reduction in morbidity and mortality throughtargeted risk management options. The traditional approach for germlinetesting has been to test for a mutation in a single gene or a limitedpanel of genes using Sanger sequencing. With advances in next-generationsequencing technology and bioinformatics analysis, testing of multiplegenes simultaneously (panel-based testing) at a cost comparable totraditional testing is possible. Panel based testing can provide betteraccuracy compared to traditional methods as well as improved diagnosticyield with analytical concordance between results from next generationsequencing (“NGS”) and the traditional Sanger method for detection ofsmall mutations, such as single nucleotide variants, small deletions,and small insertions.

Despite advancements in NGS technologies in the past years, NGS panelspossess analytical limitations which arise from sample preparation,sequencing, mapping, GC content of the targets, target size, andsequence complexity. These factors affect the relationship between readdepth and copy number, which is key to copy number variant calls, and asa result the accuracy of the use of NGS techniques for use detectingcopy number variants. Such limitations make it challenging for NGStechnologies to be used for detection of copy number variants (CNV),such as exon-level copy number variations, larger insertion variants ordeletion variants, or rearrangements. Scientific research has suggestedthat many cancers and complex diseases, such as schizophrenia, arerelated, at least in part, to copy number variants. Thus, higheraccuracy, and accounting for the effect on noise in relating sequencingdepth to copy number is especially desirable. To address this concern,some laboratories complement NGS with microarrays, which introduce theirown level of complexity and bias to the call. Copy number variantsprovide valuable information needed for better understanding andcharacterization of the hereditary susceptibility to cancer and otherdisease. As such, a method of detecting CNVs with high accuracy isdesirable.

The disclosures of all publications, patents, and patent applicationsreferred to herein are each hereby incorporated by reference in theirentireties. To the extent that any reference incorporated by referenceconflicts with the instant disclosure, the instant disclosure shallcontrol.

SUMMARY

The methods described herein are useful for determining a copy number ofan interrogated segment within a region of interest or determining acopy number variant abnormality within a region of interest. A testsequencing library can be enriched using direct targeted sequencingmethods, and the enriched sequencing library can be sequenced todetermine a number of copies at a segment within a region of interest.The methods can include using a copy number likelihood model and/or ahidden Markov model to accurately determine copy number variants. Themethods can include accounting for GC bias, sample noise and/or spuriouscapture probes.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to the interrogated segment, wherein the testsequencing library is enriched using one or more direct targetedsequencing capture probes; (b) determining a number of sequencing readsmapped to the interrogated segment; (c) determining a copy numberlikelihood model based on an expected number of sequencing reads mappedto the interrogated segment; (d) building a hidden Markov modelcomprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogatedsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of spatially adjacent segments,wherein the plurality of spatially adjacent segments comprises theinterrogated segment, and wherein the test sequencing library isenriched using a plurality of spatially adjacent direct targetedsequencing capture probes; (b) determining a number of sequencing readsmapped to each spatially adjacent segment; (c) determining a copy numberlikelihood model for each spatially adjacent segment based on anexpected number of mapped sequencing reads at the spatially adjacentsegment; (d) building a hidden Markov model comprising: (i) a pluralityof hidden states comprising a copy number for each of the spatiallyadjacent segments or a plurality of sub-segments within each of thespatially adjacent segments, (ii) a plurality of observation statescomprising the number of sequencing reads mapped to each spatiallyadjacent segment, and (iii) the copy number likelihood model for eachspatially adjacent segment; (e) parameterizing the hidden Markov modelcomprising adjusting each copy number likelihood model to fit thedetermined number of sequencing reads mapped to each spatially adjacentsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments, the method further comprises determining a mostprobable copy number of a section within the region of interest, whereinthe section comprises a plurality of spatially adjacent segmentscomprising the interrogated segment.

In some embodiments, the copy number likelihood model comprises adistribution for two or more copy number states.

In some embodiments, the copy number likelihood model comprises anegative binomial distribution, wherein the negative binomialdistribution is not a Poisson distribution.

In some embodiments, the expected number of sequencing reads is based onan average number of mapped sequencing reads at a corresponding segmentacross a plurality of sequencing libraries and an average number ofmapped sequencing reads across a plurality of segments of interestwithin the test sequencing library, wherein the average number of mappedsequencing reads at a corresponding segment across a plurality ofsequencing libraries or the average number of mapped sequencing readsacross a plurality of segments of interest within the test sequencinglibrary is a normalized average.

In some embodiments, the copy number likelihood model is adjusted toaccount for the presence of GC content bias. In some embodiments, theadjustment depends on the GC content of the capture probe correspondingto the interrogated segment or the GC content of the interrogatedsegment.

In some embodiments, the hidden Markov model comprises a transitionprobability of the copy number of the interrogated segment for a givencopy number of a spatially adjacent segment.

In some embodiments, the hidden Markov model comprises a plurality oftransition probabilities of the copy number of a sub-segment in theplurality of sub-segments within the interrogated segment for a givencopy number of a spatially adjacent sub-segment. In some embodiments,the transition probability accounts for an average length of a copynumber variant. In some embodiments, the transition probability accountsfor a prior probability of a copy number variant at the interrogatedsegment or a spatially adjacent segment. In some embodiments, theaverage length of a copy number variant or the probability of a copynumber variant at the interrogated segment are determined based onobservations in a human population.

In some embodiments, parameterizing the hidden Markov model comprisesaccounting for one or more spurious capture probes. In some embodiments,accounting for one or more spurious capture probes comprises weightingthe one or more observation states in the plurality of observationstates with a spurious capture probe indicator. In some embodiments, thespurious capture probe indicator is determined using a Bernoulliprocess. In some embodiments, accounting for one or more of the captureprobes being spurious comprises using expectation-maximization. In someembodiments, if a capture probe is determined to be spurious, thelikelihood information from that capture probe is disregarded in thecopy number likelihood model.

In some embodiments, the parameterizing of the hidden Markov modelcomprises accounting for noise in the number of mapped sequencing reads.In some embodiments, accounting for noise in the number of mappedsequencing reads comprises adjusting the copy number likelihood model.In some embodiments, adjusting the copy number likelihood model toaccount for the noise comprises an expectation-maximization step. Insome embodiments, the expectation-maximization step comprises weighing alevel of noise in the number of mapped sequencing reads from the testsequencing library. In some embodiments, the expectation-maximizationstep comprises using a Quasi-Newtonian solver. In some embodiments, themost probable copy number of the interrogated segment is not called ifthe noise in the number of mapped sequencing reads is above apredetermined threshold.

In some embodiments, sequencing reads from overlapping capture probesare merged.

In some embodiments, a Viterbi algorithm, a Quasi-Newton solver, or aMarkov chain Monte Carlo is used to determine the most probable copynumber of the interrogated segment.

In some embodiments, the method further comprises determining aconfidence of the most probable copy number of the segment.

In some embodiments, the region of interest is a region within genomicDNA.

In some embodiments, the test sequencing library is derived fromcell-free DNA.

In some embodiments, the method comprises reporting the most probablecopy number of the interrogated segment. In some embodiments, the methodcomprises reporting a copy number variant. In some embodiments, the copynumber variant is reported to a patient or a healthcare provider. Insome embodiments, the method comprises providing a medical diagnosisbased on the most probable copy number of the interrogated segment. Insome embodiments, the method comprises suggesting a treatment regimenbased on the most probable copy number of the interrogated segment.

In some embodiments, there is provided a method for determining a copynumber variant abnormality within a region of interest, comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to an interrogated segment within the region of interest,wherein the test sequencing library is enriched using one or more directtargeted sequencing capture probes; (b) determining a number ofsequencing reads mapped to the interrogated segment; (c) determining acopy number likelihood model based on an expected number of sequencingreads mapped to the interrogated segment; (d) building a hidden Markovmodel comprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogatedsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model; (g)determining a copy number variant abnormality based on the most probablecopy number of the interrogated segment.

In some embodiments, there is provided a method for determining a copynumber variant abnormality within a region of interest, comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to a plurality of spatially adjacent segments, wherein theplurality of spatially adjacent segments comprises an interrogatedsegment, and wherein the test sequencing library is enriched using aplurality of spatially adjacent direct targeted sequencing captureprobes; (b) determining a number of sequencing reads mapped to eachspatially adjacent segment; (c) determining a copy number likelihoodmodel for each spatially adjacent segment based on an expected number ofmapped sequencing reads at the spatially adjacent segment; (d) buildinga hidden Markov model comprising: (i) a plurality of hidden statescomprising a copy number for each of the spatially adjacent segments ora plurality of sub-segments within each of the spatially adjacentsegments, (ii) a plurality of observation states comprising the numberof sequencing reads mapped to each spatially adjacent segment, and (iii)the copy number likelihood model for each spatially adjacent segment;(e) parameterizing the hidden Markov model comprising adjusting eachcopy number likelihood model to fit the determined number of sequencingreads mapped to each spatially adjacent segment; and (f) determining amost probable copy number of the interrogated segment based on theparameterized hidden Markov model; (g) determining a copy number variantabnormality based on the most probable copy number of the interrogatedsegment.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of segments within a region ofinterest, wherein the test sequencing library is enriched using aplurality of capture probes, and wherein the plurality of segmentscomprises the interrogated segment; (b) determining a number ofsequencing reads mapped to each segment; (c) determining a copy numberlikelihood model for the segment based on an expected number of mappedsequencing reads at each segment, wherein the expected number of mappedsequencing reads is corrected for GC content of the segment; and (d)determining a most probable copy number of the interrogated segmentbased on the copy number likelihood model.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to the interrogated segment, wherein the testsequencing library is enriched using a plurality of capture probes; (b)determining a number of sequencing reads mapped to the interrogatedsegment; (c) determining a copy number likelihood model based on anexpected number of sequencing reads mapped to the interrogated segment,wherein the expected number of mapped sequencing reads is corrected forGC content of the interrogated segment; (d) building a hidden Markovmodel comprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogatedsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of spatially adjacent segments,wherein the plurality of spatially adjacent segments comprises theinterrogated segment, and wherein the test sequencing library isenriched using a plurality of spatially adjacent capture probes; (b)determining a number of sequencing reads mapped to each spatiallyadjacent segment; (c) determining a copy number likelihood model foreach spatially adjacent segment based on an expected number of mappedsequencing reads at the spatially adjacent segment, wherein the expectednumber of mapped sequencing reads is corrected for GC content of thespatially adjacent segment; (d) building a hidden Markov modelcomprising: (i) a plurality of hidden states comprising a copy numberfor each of the spatially adjacent segments or a plurality ofsub-segments within each of the spatially adjacent segments, (ii) aplurality of observation states comprising the number of sequencingreads mapped to each spatially adjacent segment, and (iii) the copynumber likelihood model for each spatially adjacent segment; (e)parameterizing the hidden Markov model comprising adjusting each copynumber likelihood model to fit the determined number of sequencing readsmapped to each spatially adjacent segment; and (f) determining a mostprobable copy number of the interrogated segment based on theparameterized hidden Markov model.

In some embodiments of the above methods, the capture probes are directtargeted sequencing capture probes. In some embodiments, the captureprobes enrich the sequencing library using hybrid capture techniques. Insome embodiments, the expected number of sequencing reads is correctedfor the GC content by multiplying the expected number of sequencingreads at any given segment by a GC bias correction factor for thatsegment, wherein the GC bias correction factor is determined for thetest sequencing library. In some embodiments, the GC bias correctionfactor is determined by: fitting a second order function to a pluralityof data points, wherein the data points each comprises a normalizednumber of sequencing reads mapped to a segment and the GC content ofthat segment, and wherein the plurality of data points represent aplurality of segments enriched by the capture probes in the testsequencing library; and defining the GC bias correction factor to be thenormalized number of sequencing reads determined by the second orderfunction for the GC content of the segment.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to the interrogated segment, wherein the testsequencing library is enriched using one or more capture probes; (b)determining a number of sequencing reads mapped to the interrogatedsegment; (c) determining a copy number likelihood model based on anexpected number of sequencing reads mapped to the interrogated segment;(d) building a hidden Markov model comprising: (i) one or more hiddenstates comprising a copy number corresponding to the interrogatedsegment or a plurality of sub-segments within the interrogated segment,(ii) an observation state comprising the number of sequencing readsmapped to the interrogated segment; and (iii) the copy number likelihoodmodel; (e) parameterizing the hidden Markov model by adjusting the copynumber likelihood model to fit the determined number of sequencing readsmapped to the interrogated segment and accounting for one or morespurious capture probes; and (f) determining a most probable copy numberof the interrogated segment based on the parameterized hidden Markovmodel.

In some embodiments, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of spatially adjacent segments,wherein the plurality of spatially adjacent segments comprises theinterrogated segment, and wherein the test sequencing library isenriched using a plurality of spatially adjacent direct targetedsequencing capture probes; (b) determining a number of sequencing readsmapped to each spatially adjacent segment; (c) determining a copy numberlikelihood model for each spatially adjacent segment based on anexpected number of mapped sequencing reads at the spatially adjacentsegment; (d) building a hidden Markov model comprising: (i) a pluralityof hidden states comprising a copy number for each of the spatiallyadjacent segments or a plurality of sub-segments within each of thespatially adjacent segments, (ii) a plurality of observation statescomprising the number of sequencing reads mapped to each spatiallyadjacent segment, and (iii) the copy number likelihood model for eachspatially adjacent segment; (e) parameterizing the hidden Markov modelcomprising adjusting each copy number likelihood model to fit thedetermined number of sequencing reads mapped to each spatially adjacentsegment and accounting for one or more spurious capture probes; and (f)determining a most probable copy number of the interrogated segmentbased on the parameterized hidden Markov model.

In some embodiments, accounting for one or more spurious capture probescomprises weighting the one or more observation states in the pluralityof observation states with a spurious capture probe indicator. In someembodiments, the spurious capture probe indicator is determined using aBernoulli process. In some embodiments, accounting for one or more ofthe capture probes being spurious comprises usingexpectation-maximization. In some embodiments, the most probable copynumber of the interrogated segment or the one or more sub-segments ofthe interrogated segment is not called if the capture probe associatedwith the interrogated segment is determined to be spurious. In someembodiments, the most probable copy number of the interrogated segmentor the one or more sub-segments of the interrogated segment is notcalled if the probability of a capture probe being spurious is above apredetermined threshold. In some embodiments, the capture probes aredirect targeted sequencing capture probes. In some embodiments, thecapture probes enrich the sequencing library using hybrid capturetechniques.

In some embodiments, the interrogated segment is at least 100 bases inlength.

Also provided herein is a computer system comprising a computer-readablemedium comprising instructions for carrying out any of the methodsdescribed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a flow chart of one embodiment of a method for determininga copy number of a segment.

FIG. 2A shows the sequencing read count (i.e., sequencing depth) foracross approximately 2500 segments (approximately 2500 unique captureprobes) in a single test sequencing library. FIG. 2B shows mediannormalized sequencing depth (that is, the sequencing depth for a singlesegment normalized to the median for that same segment across all testsequencing libraries) for 48 different test sequencing libraries.

FIG. 3A shows a plot of the sequencing depth variance against the meannumber of sequencing reads (“mean depth”) for approximately 2500 captureprobes used to enrich a sequencing library for a region of interest fora plurality of different samples. The data was fit using a negativebinomial distribution, wherein the negative binomial distribution is nota Poisson distribution. As a comparison, a Poisson distribution is alsoillustrated, which assumes a linear relationship between dispersion andmean depth. As can be seen in the graph, the variance to depthdistribution across the probes follows a negative binomial distributionand not simply a Poisson distribution.

FIG. 3B shows a copy number likelihood model comprising negativebinomial distributions, wherein the negative binomial distributions arenot Poisson distributions or Poisson distributions for a copy number of1, 2, or 3 copies of a segment. The distributions are probability massfunctions (pmf) as a function of the number of sequencing reads from thecapture probe corresponding with the segment. “CN”=Copy Number.

FIG. 4A shows an exemplary hidden Markov model with c₁, c₂, c₃, and c₄represent the hidden states (i.e., the most probable copy number forfour different segments) and k₁, k₂, k₃, and k₄ represent the observedstates (i.e., the number of mapped sequencing reads for eachcorresponding segment). The probabilities between the observed statesand the hidden states at each corresponding segment are indicated byp(c₁|k₁), p(c₂|k₂), p(c₂|k₂), and p(c₂|k₂), while the transitionprobabilities between the hidden states are indicated by p(c₂|c₁),p(c₃|c₂), and p(c₄|c₃). The copy number likelihood model is used toparameterize the probabilities between the observed states and thehidden states. Both sets of probabilities are optimized usingexpectation-maximization (EM).

FIG. 4B illustrates a hidden Markov model for two segments subdividedinto sub-segments. The sub-segments include hidden states, but do notinclude observed states. The transition probabilities of a sub-segmentbased on the copy number state of an adjacent sub-segment. This can bedone on a per base (or per sub-segment) segmentation.

FIG. 5A illustrates a hidden Markov model, wherein a spurious captureprobe indicator prior is placed on the observation state.

FIG. 5B illustrates priors that can be adjusted to determine if a givencapture probe is a spurious capture probe, which is used to determinethe prior b_(i) on the observed state k_(i). A Bernoulli process can beused to determine the spurious capture probe probability for each testsequencing library and how this probability can influence the spuriosityof probes for that test sequencing library.

FIG. 6A shows the determined copy number for a plurality of segmentsacross 22 genes for a less noisy test sequencing library, and FIG. 6Bshows the determined copy number for a plurality of segments across 22genes for a noisier test sequencing library. The two different testsequencing libraries were enriched with the same capture probes displaydifferent levels of noise.

FIG. 7 shows copy number calls across multiple segments within the sameregion of interest (y-axis) for several test sequencing libraries(x-axis) relying only on a copy number likelihood model. Darker shadedareas show a deviation from a copy number state of two. The boxed regionshows how a true copy number variant spans across multiple segments,whereas deviations from a copy number state of two which are onlyobserved within a segment are likely to be false positives rather thantrue copy number variants.

FIG. 8 shows copy number calls across multiple segments within the sameregion of interest (y-axis) for several test sequencing libraries(x-axis) after the determining the most probably copy number using ahidden Markov model. Darker shaded areas show a deviation from a copynumber state of two. The boxed region shows how a true copy numbervariant spans across multiple segments, and false positives areminimized. The HMM takes into consideration the effect that a copynumber state of an adjacent segment has on subsequent segments. Thisallows the model to call true copy number variants, as opposed tovariations that are observed within a single segment.

DETAILED DESCRIPTION

The methods described herein allow for accurate determination of thenumber of copies of an interrogated segment of a genome, such as a geneor gene segment. Accurate copy number calling allows for betterdiagnosis of certain genetic anomalies, which aid in making importantmedical decisions. The methods include the use of a hidden Markov model(HMM) to determine a most probable copy number for an interrogatedsegment of a test sequencing library that has been enriched using directtargeted sequencing (DTS) methods. DTS methods provide high resolutiontargeting of interrogated sequences, and the HMM caller described hereinis substantially benefitted by the large amount of collected data forcopy number calling. To further increase the accuracy of the HMM caller,sequencing depth artifacts that can arise from direct targetedsequencing methods can be accounted for. Such sequencing depth artifactsmay include, for example, GC bias correction and determination ofspurious probes. Additionally, the methods described herein provide foraccurate copy number calling when the sequencing reads are produced froma noisy sequencing library.

In some embodiments, the method for determining a copy number of aninterrogated segment within a region of interest comprising (a) mappinga plurality of sequencing reads generated from a test sequencing libraryto the interrogated segment, wherein the test sequencing library isenriched using one or more direct targeted sequencing capture probes;(b) determining a number of sequencing reads mapped to the interrogatedsegment; (c) determining a copy number likelihood model based on anexpected number of sequencing reads mapped to the interrogated segment;(d) building a hidden Markov model comprising: (i) one or more hiddenstates comprising a copy number corresponding to the interrogatedsegment or a plurality of sub-segments within the interrogated segment,(ii) an observation state comprising the number of sequencing readsmapped to the interrogated segment; and (iii) the copy number likelihoodmodel; (e) parameterizing the hidden Markov model by adjusting the copynumber likelihood model to fit the determined number of sequencing readsmapped to the interrogated segment; and (f) determining a most probablecopy number of the interrogated segment based on the parameterizedhidden Markov model. In some embodiments, the copy number likelihoodmodel is optimized to account for noise. Noise can arise, for example,from GC content bias of a test sequencing library, from preparation ofthe test sequencing library, or from hybridization by the captureprobes. In some embodiments the copy number likelihood model is astatistical distribution. In some embodiments the copy number likelihoodmodel is a negative binomial distribution (such as a generalized Poissonnegative binomial distribution, wherein the negative binomialdistribution is not simply a Poisson distribution). In some embodimentsthe hidden Markov model comprises a transition probability of the copynumber of the interrogated segment for a given copy number of aspatially adjacent segment. In some embodiments the hidden Markov modelcomprises a plurality of transition probabilities of the copy number ofa sub-segment in the plurality of sub segments within the interrogatedsegment for a given copy number of a spatially adjacent sub-segment. Insome embodiments a transition probability of the hidden Markov modelaccounts for an average length of a copy number variant and aprobability of a copy number variant at the segment.

Further provided herein is a method for determining a copy number of aninterrogated segment within a region of interest comprising: (a) mappinga plurality of sequencing reads generated from a test sequencing libraryto a plurality of spatially adjacent segments, wherein the plurality ofspatially adjacent segments comprises the interrogated segment, andwherein the test sequencing library is enriched using a plurality ofspatially adjacent direct targeted sequencing capture probes; (b)determining a number of sequencing reads mapped to each spatiallyadjacent segment; (c) determining a copy number likelihood model foreach spatially adjacent segment based on an expected number of mappedsequencing reads at the spatially adjacent segment; (d) building ahidden Markov model comprising: (i) a plurality of hidden statescomprising a copy number for each of the spatially adjacent segments ora plurality of sub-segments within each of the spatially adjacentsegments, (ii) a plurality of observation states comprising the numberof sequencing reads mapped to each spatially adjacent segment, and (iii)the copy number likelihood model for each spatially adjacent segment;(e) parameterizing the hidden Markov model comprising adjusting eachcopy number likelihood model to fit the determined number of sequencingreads mapped to each spatially adjacent segment; and (f) determining amost probable copy number of the interrogated segment based on theparameterized hidden Markov model.

Also described herein are methods for determining a copy number variantabnormality within a region of interest, comprising (a) mapping aplurality of sequencing reads generated from a test sequencing libraryto an interrogated segment within the region of interest, wherein thetest sequencing library is enriched using one or more direct targetedsequencing capture probes; (b) determining a number of sequencing readsmapped to the interrogated segment; (c) determining a copy numberlikelihood model based on an expected number of sequencing reads mappedto the interrogated segment; (d) building a hidden Markov modelcomprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogatedsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model; (g)determining a copy number variant abnormality based on the most probablecopy number of the interrogated segment.

In addition, there is provided herein a method for determining a copynumber variant abnormality within a region of interest, comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to a plurality of spatially adjacent segments, wherein theplurality of spatially adjacent segments comprises an interrogatedsegment, and wherein the test sequencing library is enriched using aplurality of spatially adjacent direct targeted sequencing captureprobes; (b) determining a number of sequencing reads mapped to eachspatially adjacent segment; (c) determining a copy number likelihoodmodel for each spatially adjacent segment based on an expected number ofmapped sequencing reads at the spatially adjacent segment; (d) buildinga hidden Markov model comprising: (i) a plurality of hidden statescomprising a copy number for each of the spatially adjacent segments ora plurality of sub-segments within each of the spatially adjacentsegments, (ii) a plurality of observation states comprising the numberof sequencing reads mapped to each spatially adjacent segment, and (iii)the copy number likelihood model for each spatially adjacent segment;(e) parameterizing the hidden Markov model comprising adjusting eachcopy number likelihood model to fit the determined number of sequencingreads mapped to each spatially adjacent segment; and (f) determining amost probable copy number of the interrogated segment based on theparameterized hidden Markov model; (g) determining a copy number variantabnormality based on the most probable copy number of the interrogatedsegment.

In another aspect, there is provided a method for determining a copynumber of an interrogated segment within a region of interestcomprising: (a) mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of segments within a region ofinterest, wherein the test sequencing library is enriched using aplurality of capture probes, and wherein the plurality of segmentscomprises the interrogated segment; (b) determining a number ofsequencing reads mapped to each segment; (c) determining a copy numberlikelihood model for the segment based on an expected number of mappedsequencing reads at each segment, wherein the expected number of mappedsequencing reads is corrected for GC content bias of the segment; and(d) determining a most probable copy number of the interrogated segmentbased on the copy number likelihood model.

In some embodiments, there is a method for determining a copy number ofan interrogated segment within a region of interest comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to the interrogated segment, wherein the test sequencing libraryis enriched using a plurality of capture probes; (b) determining anumber of sequencing reads mapped to the interrogated segment; (c)determining a copy number likelihood model based on an expected numberof sequencing reads mapped to the interrogated segment, wherein theexpected number of mapped sequencing reads is corrected for GC contentof the interrogated segment; (d) building a hidden Markov modelcomprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogatedsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments, there is a method for determining a copy number ofan interrogated segment within a region of interest comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to a plurality of spatially adjacent segments, wherein theplurality of spatially adjacent segments comprises the interrogatedsegment, and wherein the test sequencing library is enriched using aplurality of spatially adjacent capture probes; (b) determining a numberof sequencing reads mapped to each spatially adjacent segment; (c)determining a copy number likelihood model for each spatially adjacentsegment based on an expected number of mapped sequencing reads at thespatially adjacent segment, wherein the expected number of mappedsequencing reads is corrected for GC content of the spatially adjacentsegment; (d) building a hidden Markov model comprising: (i) a pluralityof hidden states comprising a copy number for each of the spatiallyadjacent segments or a plurality of sub-segments within each of thespatially adjacent segments, (ii) a plurality of observation statescomprising the number of sequencing reads mapped to each spatiallyadjacent segment, and (iii) the copy number likelihood model for eachspatially adjacent segment; (e) parameterizing the hidden Markov modelcomprising adjusting each copy number likelihood model to fit thedetermined number of sequencing reads mapped to each spatially adjacentsegment; and (f) determining a most probable copy number of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments, there is a method for determining a copy number ofan interrogated segment within a region of interest comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to the interrogated segment, wherein the test sequencing libraryis enriched using one or more capture probes; (b) determining a numberof sequencing reads mapped to the interrogated segment; (c) determininga copy number likelihood model based on an expected number of sequencingreads mapped to the interrogated segment; (d) building a hidden Markovmodel comprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogated segmentand accounting for one or more spurious capture probes; and (f)determining a most probable copy number of the interrogated segmentbased on the parameterized hidden Markov model.

In some embodiments, there is a method for determining a copy number ofan interrogated segment within a region of interest comprising: (a)mapping a plurality of sequencing reads generated from a test sequencinglibrary to a plurality of spatially adjacent segments, wherein theplurality of spatially adjacent segments comprises the interrogatedsegment, and wherein the test sequencing library is enriched using aplurality of spatially adjacent direct targeted sequencing captureprobes; (b) determining a number of sequencing reads mapped to eachspatially adjacent segment; (c) determining a copy number likelihoodmodel for each spatially adjacent segment based on an expected number ofmapped sequencing reads at the spatially adjacent segment; (d) buildinga hidden Markov model comprising: (i) a plurality of hidden statescomprising a copy number for each of the spatially adjacent segments ora plurality of sub-segments within each of the spatially adjacentsegments, (ii) a plurality of observation states comprising the numberof sequencing reads mapped to each spatially adjacent segment, and (iii)the copy number likelihood model for each spatially adjacent segment;(e) parameterizing the hidden Markov model comprising adjusting eachcopy number likelihood model to fit the determined number of sequencingreads mapped to each spatially adjacent segment and accounting for oneor more spurious capture probes; and (f) determining a most probablecopy number of the interrogated segment based on the parameterizedhidden Markov model.

In some embodiments, the methods described herein further comprisereporting the most probable copy number of the interrogated segment or asub-segment of the interrogated segment. The methods can also includereporting a copy number variant, which can be reported to a patient or ahealthcare provider (such as a doctor or a hospital). In someembodiments, the methods described herein further comprise providing amedical diagnosis based on the most probable copy number of theinterrogated segment or a sub-segment of the interrogated segment. Insome embodiments, the methods described herein further comprisesuggesting a treatment regimen based on the most probable copy number ofthe interrogated segment or a sub-segment of the interrogated segment.

Sequencing libraries derived from patient samples can be sequenced toobtain a number of sequencing reads. The copy number of a segment isrelated to the sequencing depth (that is, the number of sequencing readsor a normalized number of sequencing reads) at that segment. The presentdisclosure describes a method of using the sequencing depth at thesegment to determine the presence of a copy number state at the segment.The sequencing depth may be obtained by determining the sequencing readsmapped to that segment. The sequencing depth may be obtained bydetermining the sequencing reads mapped to a capture probe correspondingto that segment. The method takes into consideration several factorsassociated with the sequencing technology to optimize the call so thatit is more accurate.

Determining the mapped number of sequencing reads for a segment dependsat least in part, to the actual copy number state of a segment. The vastmajority of genetic regions in mammals are diploid and as such it isexpected that, generally, there will be two copies of a genetic segment.This might not always be the case. For example, some regions of thegenome are not diploid due to their location (being located on the Ychromosome for example). Other regions of the genome lose their diploidyas a result of functional specialization of some cells, such as immunecells, that result in genomic re-arrangements. However, regardless ofthese deviations from the norm, the copy number state of most genomicregions is expected to be two, and a deviation from a copy number stateof two is expected to be reflected in the number of mapped sequencingreads.

Mapping sequencing reads to a segment can be preceded by one or moreupstream steps, such as sample preparation, including fragmentation,formation of the sequencing library (for example, by ligating sequencingadapters to the nucleic acid molecules in the sequencing library), andsequencing the sequencing library. Noise in the sequencing depth at anyof these upstream steps can introduce noise to the number of sequencingreads. Furthermore, the various capture probes in a capture probelibrary may not behave identically. For example, certain segments withinthe region of interest may not allow for ideal capture probe design,which can lead to spurious capture probes. Thus, using the determinednumber of mapped sequencing reads to determine the copy number state ofa segment is less direct than recognizing the existing dependencybetween the copy number state of a segment and the determined number ofmapped sequencing reads at the segment. The methods of the presentinvention allow for a copy number call of an interrogated segment withinthe region of interest to be made using a hidden Markov model, which isparameterized and optimized to account for the dependency between thenumber of mapped sequencing reads and the copy number state of thesegment. The hidden Markov model can also account for various sourcesand levels of confounders. This method allows for a particularlyeffective and efficient process for determining copy numbers ofinterrogated segments or sub-segments within a region of interest, andfor determining a copy number variant abnormality within the region ofinterest.

In some embodiments of the present invention, the sequencing library isenriched for the region of interest using direct targeted sequencing.Direct targeted sequencing uses a capture probe library comprising aplurality of capture probes that hybridize to nucleic acid molecules inthe sequencing library. The capture probes are designed to hybridize tosegments within the region of interest, and each capture probe has acorresponding segment. The region of interest is therefore determined bythe capture probes used to enrich the sequencing library. The captureprobes are extended using the nucleic acid molecules hybridized to thecapture probe as a template. The extended capture probe can then besequenced to obtain the sequence a portion (that is, the portioncorresponding to the segment from the region of interest) of the nucleicacid molecule. Because the sequence of the capture probe itself isdetermined, the segment corresponding to the capture probe beginsfollowing the terminus of the capture probe. In some embodiments, theextended capture probe is amplified to obtain additional copies.Amplification of the extended capture probe can also introduce artifactsin the sequencing depth, which can be normalized as described herein.U.S. Pat. No. 9,309,556, entitled “Direct Capture, Amplification andSequencing of Target DNA using Immobilized Primers”; U.S. Pat. No.9,092,401, entitled “System and Method for Detecting Genetic Variation”;U.S. Patent App. No. 2014/0024541, entitled “Methods and Compositionsfor High-throughput Screening”; Myllykangas et al. “Efficient targetedresequencing of human germline and cancer genomes byoligonucleotide-selective sequencing.” Nat Biotechnol. 29(11):1024-7(2011); and Hopmans et al., “A programmable method for massivelyparallel targeted sequencing.” Nucleic Acids Res. 42(10):e88 (2014)describe embodiments of direct targeted sequencing. Direct targetedsequencing need not be performed using surface-based methods, but canalso be performed in solution.

In some embodiments, the sequencing library is enriched for the regionof interest using methods other than direct targeted sequencing. Forexample, the sequencing library can be enriched using hybrid capturetechniques, which include combining the sequencing library with acapture probe library to hybridize the capture probes with nucleic acidmolecules in the sequencing library. The hybridized nucleic acidmolecules can then be isolated from the rest of the sequencing library(for example, by using biotinylated capture probes and usingstreptavidin beads to separate the hybridized molecules). The nucleicacid molecules in the enriched sequencing library can then be sequenced.Because the nucleic acid molecules from the sequencing library aredirectly sequenced (as opposed to direct targeted sequencing methods),the capture probes do not necessarily correspond with specific segmentswithin the region of interest. Instead, the sequencing depth at anygiven base within the region of interest can be determined by the numberof sequencing reads at that base.

Provided herein are definitions, explanations, examples and descriptionsthat allow one skilled in the art to understand the scope of the methodsprovided, and enable one skilled in the art to practice the invention.It is to be understood that one, some or all of the properties of thevarious embodiments described herein may be combined to form otherembodiments of the present invention. The section headings used hereinare for organizational purposes only and are not to be construed aslimiting the subject matter described.

Definitions

As used herein, the singular forms “a,” “an,” and “the” include theplural reference unless the context clearly dictates otherwise.

Reference to “about” or “approximately” a value or parameter hereinincludes (and describes) variations that are directed to that value orparameter per se. For example, description referring to “about X”includes description of “X.”

The term “average” as used herein refers to either a mean or a median,or any value used to approximate the mean or the median, unless thecontext clearly indicates otherwise.

A “capture probe” refers to a DNA or RNA which hybridize to nucleic acidmolecules having segments with complementary sequences (or sufficientlycomplementary sequences to allow for hybridization under normalhybridization conditions) to the probes. The nucleic acid molecules arepresent in a sequencing library.

“Copy number likelihood” refers to the likelihood of a copy number stateat a segment or sub-segment of interest. The copy number likelihood canbe determined by use of a statistical model.

“Copy number likelihood model” refers to a statistical model used todetermine a likelihood of one or more copy number states of a segment ofinterest, given a number of mapped sequencing reads at that segment. Thecopy number likelihood model includes a statistical distribution foreach copy number state covered by the model, and each distributionreflects the probability that the copy number state is correct for agiven number of mapped sequencing reads.

“Copy number variant” or “CNV” refers to a deviation in the copy numberstate from a wild type. A “wild-type” as used herein refers to apredetermined copy number state for a particular segment that isconsidered normal. The determination of what is “wild-type” can be madebased on human, mammal or other animal population data. Thedetermination of what a “wild-type” is can also be made based onreference runs, internal experiments and data generated from suchexperiments.

A “direct targeted sequencing capture probe” is a capture probe that isused to enrich a sequence from a sequencing library using directtargeted sequencing.

An “interrogated segment” refers to a segment for which it is desirableto determine the copy number state. The interrogated segment is within aregion of interest. The interrogated segment can be divided intosub-segments. Such sub-segments may be as small as one base pair, but nolonger than the length of the interrogated segment. In the context ofthe hidden Markov model, the copy number state of the interrogatedsegment is a hidden state of the model. It is desirable that by solvingthe hidden Markov model a most probable copy number state for theinterrogated segment can be determined.

A “noisy sequencing library” or “noise” from a sequencing library refersto a sequencing library that generates poor data across one or morecapture probes. During preparation or sequencing of the sequencinglibrary, several sources of noise exist. For example oligonucleotidecollection, storage, or fragmentation can compromise the integrity ofthe oligonucleotide, which in turn can affect how the oligonucleotide isamplified, sequenced, and mapped. This leads to “noise” which comes fromthe preparation or inherent characteristics of the sequencing library.

“Optimization” or “optimizing” as used herein refers to finding the bestsolution for a given objective given pre-determined constrains.Adjusting a model comprises optimizing a model. Maximizing is a type ofoptimizing. A model always comprises a plurality of parameters.

Optimizing a model is to find a set of parameters that would maximizethe likelihood of correctly estimating an unknown parameter of themodel. It is also understood that optimization may include severalsteps. For example a parameter in the hidden Markov model may undergoseveral rounds of expectation maximization.

A “segment” refers to a nucleotide chain comprising two or more bases. Asegment can be sub-divided into one or more “sub-segments.” A“sub-segment” can be as small as one nucleotide but not longer than thesegment in which is it is located. A region of interest can be dividedinto one or more segments. The segments can be, but need not be,contiguous. Therefore a region of interest can optionally includenon-contiguous sub-regions. The segments can be of the same length or ofdifferent lengths. Two or more segments within a region of interest canbe grouped to make a section within the region of interest. The segmentsthat make up a section within the region of interest may be, but neednot be contiguous.

A “spurious capture probe” refers to an unreliable capture probe becauseit generates artifacts in the number of sequencing reads. The artifactscan be due to sub-par sequencing reads, inconsistent sequencing reads,sequencing reads of length that fall below a predetermined level, anumber of sequencing reads that fall below a predetermined level, ordisplays poor quality when compared to other capture probes.

“Spatially adjacent segments” refer to a set of sequential segments thatare located within the same chromosome, but need not be contiguous. Thatis, two spatially adjacent segments can be separated by a number ofintervening nucleotides but not by intervening segments outside of theset of spatially adjacent segments. The copy number of any interveningnucleotides if the two spatially adjacent segments are not contiguousmay be inferred through the hidden Markov model. “Spatially adjacentcapture probes,” including “spatially adjacent direct targetedsequencing capture probes,” refer to capture probes that correspond tothe spatially adjacent segments.

It is understood that aspects and variations of the invention describedherein include “consisting” and/or “consisting essentially of” aspectsand variations.

Where a range of values is provided, it is to be understood that eachintervening value between the upper and lower limit of that range, andany other stated or intervening value in that stated range, isencompassed within the scope of the present disclosure. Where the statedrange includes upper or lower limits, ranges excluding either of thoseincluded limits are also included in the present disclosure.

Methods of Determining a Copy Number

The present disclosure provides methods to determine the copy number ofan interrogated segment (or sub-segment of the interrogated segment) ofa region of interest, or a copy number variant abnormality within aregion of interest, based on the determined number of mapped sequencingreads at that segment. The methods include determining a copy numberlikelihood model based on an expected number of mapped sequencing readsfor one or more copy number states. Expectation-Maximization (EM) can beused to enable latent parameter estimation and optimization of themodel. Several additional steps and adjustments to the model can be usedto account for other factors that affect the relationship between a copynumber and the number of mapped sequencing reads. The information isused to parameterize the hidden Markov model which can then be used todetermine a most probable copy number state at an interrogated segment.Methods for building the copy number likelihood model,Expectation-Maximization implementation, adjustment to the model toaccount for multiple factors, parameterization of the hidden Markovmodel as well as methods of solving the various steps and the modeloverall, are provided generally below. In one preferred embodiment theefficiency and reliability of the hidden Markov model, relies on the useof Expectation-Maximization (EM) to enable parameter estimation forseveral latent variables.

In brief, the methods for determining a copy number of a segment orsub-segment include (1) determining the number of sequencing readsmapped to an interrogated segment; (2) building and parameterizing ahidden Markov model by determining a copy number likelihood model; and(3) determining a most probable copy number of the interrogated segment(or a sub-segment of the interrogated segment) using the parameterizedhidden Markov model. In some embodiments, the methods provided hereinalso include steps to refine the model by accounting for confoundingeffects that may arise during the process.

In some embodiments of the methods described herein, a hidden Markovmodel is used to determine the most probable copy number state of asegment. The hidden Markov model can include: a hidden layer whichcomprises the copy number state of a segment of interest; an observationlayer, which comprises the mapped number of sequencing reads; atransition probabilities between the copy number state in the hiddenlayer and mapped number of sequencing reads (probability inter-layers);and a transition probabilities of a copy number state of a segment giventhe copy number state of a preceding adjacent segment (probabilityintra-hidden layer). FIG. 1 illustrates one embodiment of a method fordetermining a copy number of an interrogated segment within a region ofinterest. At step 110, sequencing reads generated for a test sequencinglibrary are mapped to a segment or segments within a region, or regionsof interest. At step 120 the number of sequencing reads mapped at thesegment(s) within region(s) of interest is determined. At step 130 acopy number likelihood model is determined which is used to set thetransition probability of a copy number state given the observed numberof mapped sequencing reads. At step 140, a hidden Markov model is builtwhich comprises the hidden layer, the observation layer and transitionprobabilities. At step 150 the hidden Markov model is parameterized. Inits simplest form, the hidden Markov model comprises at least twounknown parameters: the copy number state and the transitionprobabilities between the copy number state and observed number ofsequencing reads, which are determined by the copy number likelihoodmodel. Expectation-Maximization is used to determine these parametersbased on the best fit of the data (that is, parameterize the model) andto determine the most probable copy number. In the model it is desirableto maximize the probability of a copy number state given the observednumber of sequencing reads, to determine the most probable copy numberof the segment. In step 160 a most probable copy number state of thesegment is determined. The process may consider other variables thataffect the observation states, such as GC content bias, spuriosity of acapture probe associated with a segment, noisy test sequencing librarieswhich affect the transition probabilities. The additional variables aretreated as latent and determined by EM given the available data. Thetransition probabilities are then adjusted to account for these othervariables. The EM process can be cumulative (adjusting for all variablesat once) or it can adjust for the variables in separate EM iterationsbefore the HMM is solved to determine a most probable copy number stateof the segment.

Determining a Number of Mapped Sequencing Reads

In some embodiments, the methods described herein include mapping aplurality of sequencing reads generated from a test sequencing libraryto an interrogated segment. In some embodiments, the methods describedherein include mapping a plurality of sequencing reads generated from atest sequencing library to a plurality of spatially adjacent segments,wherein the plurality of spatially adjacent segments includes theinterrogated segment. The sequencing library is enriched for a region ofinterest, such as by direct targeted sequencing. The mapped sequencingreads can be counted to determine a number of sequencing reads that aremapped to the interrogated segment or the spatially adjacent segments.

The spatially adjacent segments are located within the same chromosome.In some embodiments, the spatially adjacent segments are located withinthe same chromosome region. In some embodiments, the spatially adjacentsegments are located within the same gene. In some embodiments, thespatially adjacent segments are located within the same region ofinterest. In some embodiments, the spatially adjacent segments arelocated within the same portion within the region of interest.

The sequencing library can be sequenced to generate the plurality ofsequencing reads, which can be mapped to a region of interest. Thesequencing library includes a plurality of nucleic acid fragments, whichcan be isolated from bodily fluids such as blood, plasma, saliva, urineor from tissue or cultured cells. The nucleic acid fragments can be froman animal. The nucleic acid fragments can be from a mammal, for example,from a human. In a preferred embodiment the test sequencing libraryincludes a plurality of nucleic acid fragments isolated from a patient.The nucleic acid molecules in the sequencing library can be ligated tosequencing adapters, which may aid alignment in certain sequencingmethods. For example the adapters may be indexed, and the indexing maybe used to aid alignment of the sequences. The sequencing library can beenriched (such as through direct targeted sequencing) for the region ofinterest, either before or after ligating the nucleic acid molecules tothe sequencing adapters.

The nucleic acid fragments in the test sequencing library may be RNA orDNA nucleic acid fragments. The nucleic acid fragments may be cell-freeDNA. In some embodiments, the cell-free DNA comprises fetal cell-freeDNA. In some embodiments, the cell-free DNA comprises circulating tumorcell-free DNA.

The nucleic acid fragments in the sequencing library include the regionof interest. The region of interest can be a full genome or any portionof the genome. In some embodiments the region of interest comprises oneor more chromosomes. In some embodiments the region of interestcomprises one or more genes of interest (such as 2 or more, 3 or more, 4or more, 5 or more, about 10 or more, about 15 or more, about 20 ormore, about 30 or more, about 40 or more, about 50 or more, about 75 ormore, about 100 or more, about 150 or more, about 200 or more, about 250or more genes, about 300 or more, about 350 or more, about 400 or more,about 450 or more, about 500 or more, about 550 or more, about 600 ormore, about 650 or more, about 700 or more, about 750 or more, about 800or more, about 850 or more, about 900 or more, about 950 or more, orabout 1000 or more). The one or more genes of interest may be any geneassociated with a disease. The one or more genes of interest may includeany gene associated with a hereditary disease. The one or more genes ofinterest may include a gene associated with a form of cancer, such as ahereditary cancer. In some embodiments, the region of interest comprisesone or more exons (such as 2 or more, 3 or more, 4 or more, 5 or more,10 or more, 15 or more, 20 or more, 30 or more, 40 or more, 50 or more,75 or more, 100 or more, 150 or more, 200 or more, or 250 or more, 500or more, 1000 or more, or 2000 or more exons). In some embodiments, theregion of interest comprises a gene or a portion of a gene, an exon, ora portion of an exon, selected from the group consisting of APC, ATM,BARD1, BMPR1A, BRCA1, BRCA2, BRIPI, CDH1, CDK4, CDKN2A, CHEK2, EPCAM,GREM1, MEN1, MLH1, MRE11A, MSH2, MSH6, MUTYH, NBN, PALB2, PMS2, POLD1,POLE, PTEN, RAD50, RAD51C, RAD51D, RET, SDHA, SDHB, SDHC, SMAD4, STK11,TP53, VHL, PEX10, MTHFR, ALPL, HMGCL, DHDDS, PPT1, MPL, WACHC, POMGNT1,CPT2, ALG6, RPE65, ACADM, DPYD, AGL, SLC35A3, DBT, PHGDH, CTSK, NTRK1,NPHS2, LAMC2, LAMB3, USH2A, PHYH, ERCC6, PCDH15, LIPA, HOGA1, OAT, TH,HBB, SMPD1, TPP1, KCNJ11, ABCC8, USH1C, RAG2, RAPSN, TMEM216, PYGM,BBS1, PC, TCIRG1, CPT1A, DHCR7, MYO7A, MED17, PTS, SLC37A4, HYLS1, PFKM,BBS10, GNPTAB, PAH, MMAB, ACADS, PUS1, GJB2, GJB6, SGCG, SACS, ATP7B,CLN5, PCCA, ZFYVE26, VSX2, NPC2, GALC, SERPINA1, VRK1, TECPR2, SLC12A6,IVD, CAPN3, CLN6, NR2E3, HEXA, MPI, FAH, MESP2, BLM, GNPTG, MEFV, PMM2,CLN3, BBS2, TAT, CYBA, FANCA, VPS53, ASPA, CTNS, ACADVL, ALDH3A2, PEX12,NAGLU, G6PC, SGCA, MKS1, DNAI2, GALK1, GAA, SGSH, NPC1, LAMA3, LOXHD1,MCOLN1, MAN2B1, GCDH, NPHS1, BCKDHA, OPA3, FKRP, HADHA, LRPPRC, FAM161A,ATP6V1B1, DYSF, ALMS1 , NEB, CERKL, CPS1, BCS1L, CYP27A1, COL4A4,COL4A3, AGXT, NDUFAF5, ADA, RTEL1, HLCS, CBS, AIRE, TRAMU, MLC1, TYMP,ARSA, SUMF1, XPC, BTD, GLBLAMT, GBE1, HGD, PCCB, HPS3, CLRN1, BCHE, IDUA, EVC2, EVC, SEPSECS, SGCB, MTTP, BBS12, MMAA, AGA, F11, NDUFS6,DNAH5, NDUFS4, ERCC8, HEXB, HSD17B4, SLC22A5, SLC26A2, SGCD, PROP1,ADAMTS2, PEX6, MUT, PKHD1, EYS, SLC17A5, BCKDHB, RARS2, LAMA2, ARG1,PEX7, ASL, PEX1, SAMD9, ASNS, SLC26A4, DLD, CFTR, CLN8, STAR, HGSNAT,TTPA, PEX2, CNGB3, VPS13B, CYP11B1, CYP11B2, GLDC, DNAI1, GALT, RMRP,GNE, GRHPR, VPS13A, FANCC, XPA, ALDOB, FKTN, IKBKAP, ASS1, RS1, NR0B1,DMD, OTC, IL2RG, ATP7A, CHM, GLA, COL4A5, IDS, MTM1, ABCD1, or acombination thereof.

The region of interest can be divided into a plurality of segments. Eachsegment can be further divided into sub-segments. A sub-segment may be 1or more nucleotides in length. The segments within the region ofinterest may be but need not be contiguous. For example, in someembodiments, the region of interest comprises 1 or more non-contiguoussegments, 2 or more non-contiguous segments, 3 or more non-contiguoussegments, 4 or more non-contiguous segments, 5 or more non-contiguoussegments, 10 or more non-contiguous segments, 25 or more non-contiguoussegments, 50 or more non-contiguous segments, 100 or more non-contiguoussegments, 150 or more non-contiguous segments, 200 or morenon-contiguous segments, 250 or more non-contiguous segments, 300 ormore non-contiguous segments, 350 or more non-contiguous segments, 400or more non-contiguous segments, 450 or more non-contiguous segments,500 or more non-contiguous segments, 550 or more non-contiguoussegments, 600 or more non-contiguous segments, 650 or morenon-contiguous segments, 700 or more non-contiguous segments, 750 ormore non-contiguous segments, 800 or more non-contiguous segments, 850or more non-contiguous segments, 900 or more non-contiguous segments,950 or more non-contiguous segments, or 1000 non-contiguous segments. Insome embodiments, each of the non-contiguous segments comprises 1 ormore contiguous bases, 2 or more contiguous bases, 3 or more contiguousbases, 4 or more contiguous bases, or 5 or more contiguous bases. Forexample, in some embodiments each of the non-contiguous segmentscomprises 1 to about 20 contiguous bases (such as 1 to about 10contiguous bases, or about 1 to about 5 contiguous bases). In someembodiments the region of interest comprises 1 or more contiguoussegments, 2 or more contiguous segments, 3 or more contiguous segments,4 or more contiguous segments, 5 or more contiguous segments, 10 or morecontiguous segments, 25 or more contiguous segments, 50 or morecontiguous segments, 100 or more contiguous segments, 150 or morecontiguous segments, 200 or more contiguous segments, 250 or morecontiguous segments, 300 or more contiguous segments, 350 or morecontiguous segments, 400 or more contiguous segments, 450 or morecontiguous segments, 500 or more contiguous segments, 550 or morecontiguous segments, 600 or more contiguous segments, 650 or morecontiguous segments, 700 or more contiguous segments, 750 or morecontiguous segments, 800 or more contiguous segments, 850 or morecontiguous segments, 900 or more contiguous segments, 950 or morecontiguous segments, or 1000 contiguous segments. In some embodiments,each of the contiguous segments comprises 1 or more contiguous bases, 2or more contiguous bases, 3 or more contiguous bases, 4 or morecontiguous bases, or 5 or more contiguous bases. For example, in someembodiments each of the non-contiguous segments comprises 1 to about 20contiguous bases (such as 1 to about 10 contiguous bases, or about 1 toabout 5 contiguous bases). In some embodiments the region of interestcomprises a combination of non-contiguous and contiguous segments. Insome embodiments, the region of interest comprises only one segment. Insome embodiments the region of interest comprises at least one segment.In some embodiments the region of interest comprises at least twosegments. In some embodiments the region of interest comprises at leasttwo segments which are adjacent. In some embodiments one segment withina first region of interest may be adjacent to a segment in a secondregion of interest adjacent to the first region of interest.

The region of interest may be enriched with one or more capture probes.The reference location of the capture probes with respect to a region ofinterest is known. For example, the capture probes comprise a referencesequence that corresponds to pre-determined probe coordinates. In someembodiments the region of interest is divided into segments based on thelocation of capture probes (that is the capture probe corresponds with asegment).The capture probe comprises the reference sequence thatcorresponds to the probe coordinates. For example, the first nucleotideof a segment may coincide with the first nucleotide of a sequencehybridizing to the 3′ end of a capture probe. In some embodiments thefirst nucleotide of a segment coincides with the first nucleotide of asequence hybridizing to the 5′ end of a capture probe. In someembodiments the region of interest comprises two spatially adjacentsegments. A segment within a region of interest may be divided intosub-segments. A sub-segment may be as small as one nucleotide can be aslong as the segment. Sub-segments may overlap. For example a firstsub-segment may be the first nucleotide of a segment plus one downstreamnucleotide. A second sub-segment may comprise the first sub-segment plusan additional downstream nucleotide. In some embodiments, a segment of nnucleotides of length comprises n−1 sub-segments, wherein eachsubsequent sub-segment is 1 nucleotide longer than the previous. In someembodiments a segment of n nucleotides of length comprises nsubsegments, wherein each sub-segment is 1 nucleotide in length.

The region of interest comprises at least one interrogated segment. Theinterrogated segment is a segment for which it is desirable to know thecopy number. The copy number state of an interrogated segment is anunknown state and solving the hidden Markov model determines the mostprobable copy number of an interrogated segment. Like other segments, aninterrogated segment may be divided into sub-segments. In someembodiments the first nucleotide of an interrogated segment coincideswith the first nucleotide of a sequence hybridizing to the 5′ end of acapture probe. In some embodiments the first nucleotide of aninterrogated segment coincides with the first nucleotide of a sequencehybridizing to the 3′ end of a capture probe. In some embodiments theinterrogated segment comprises the sequence spanning two spatiallyadjacent capture probes. In a preferred embodiment the interrogatedsegment comprises the nucleotide sequence between two adjacent captureprobes, with the first nucleotide of the sequence being the firstnucleotide hybridizing to the 5′ end or the 3′ end of the capture probeand the last nucleotide of the segment being contiguous to the firstnucleotide hybridizing to the 5′ end or the 3′ end of a spatiallyadjacent probe.

The test sequencing library can be sequenced using next generationsequencing to generate the sequencing reads. Next generation sequencingtechnologies are well known in the art. The test sequencing library canbe sequenced using a high-throughput sequencer, such as an IlluminaHiSeq2500, Illumina HiSeq3000, Illumina HiSeq4000, Illumina HiSeqX,Roche 454, PacBio Sequel System PacBio RS II, or Life Technologies IonProton sequencing systems can also be used. Other methods of sequencingare known in the art.

In some embodiments, the sequencing library is enriched with one or morecapture probes by direct targeted sequencing. In direct targetedsequencing, capture probes hybridize specific target regions of nucleicacid molecules from within a sequencing library. This method enablesenrichment of target regions and allows subsequent sequencing efforts tofocus on relevant genomic regions or transcripts of interest. Enrichingthe target regions with capture probes for the region of interest allowsfor more efficient high throughput sequencing of the region of interest.The efficiency keeps the overall costs of sequencing test sequencinglibraries down while maintaining or increasing the sensitivity andspecificity of a diagnostic test or screen. The capture probes can beselected based on the region of interest such that those nucleic acidmolecules in the sequencing library containing a portion of the regionof interest hybridize to the capture probes and can be enriched, whereasthose nucleic acid molecules in the sequencing library that do notcontain a portion of the region of interest do not hybridize to thecapture probes and are not enriched.

In direct targeted sequencing, capture probes that hybridize to a targetsequence adjacent to the corresponding segment within the region ofinterest are combined with the sequencing library, thereby hybridizingthe capture probes to the nucleic acid molecules comprising to thetarget sequence. In direct targeted sequencing methods, the captureprobe is extended using the nucleic acid molecule as a template, and theextended capture probe is sequenced. Since the extended capture probe(or amplified copies of the extended capture probe) itself is sequenced,the sequence of the capture probe is not interpreted as the sequencearising from the test sequencing library, although it can be used to aidsequence alignment.

Other methods for enriching sequencing libraries using capture probesare generally known in the art, and can include hybrid capturetechniques (e.g., using biotinylated capture probes), and PCRamplification using capture probes as PCR primers.

In some embodiments, hybrid capture techniques are used to enrich theregion of interest by combining capture probes that are substantiallycomplementary to a portion of the region of interest with the sequencinglibrary, thereby hybridizing the capture probes to nucleic acidmolecules comprising the portion of the region of interest. The nucleicacid molecules that hybridize to the capture probes can be isolated fromnon-hybridized nucleic acid molecules (for example, by pull-downmethods). The hybridized complex can be denatured and the enrichednucleic acid molecules from the sequencing library can be sequenced. Insome embodiments, the enriched nucleic acid molecules are re-enriched ina second (or more) round of hybridization to the capture probes,isolation and denaturation before being sequenced. Optionally, thenucleic acid molecules in the sequencing library can be amplified (forexample, by PCR) either before or after enrichment.

In some embodiments, one or more of the capture probes are attached toan additional oligonucleotide (such as a primer binding site or otherspecialized nucleic acid segment). In some embodiments, the captureprobes in the capture probe library are DNA oligonucleotides, RNAoligonucleotides, or a mixture of DNA oligonucleotides and RNAoligonucleotides. In some embodiments the capture probes are about10-100 bases in length. In some embodiments the capture probes are about20-60 bases in length. In some embodiments the capture probes are about30-50 bases in length. In some embodiments the capture probes are 40bases in length.

The number of capture probes in the capture probe library can depend onthe size of the region of interest, as a larger region of interestgenerally requires a larger number of capture probes for adequatecoverage. In some embodiments, the capture probe library comprises about10 or more unique capture probes (such as about 50 or more, about 100 ormore, about 250 or more, about 500 or more, about 1000 or more, about2500 or more, about 5000 or more, about 10,000 or more, about 25,000 ormore, about 50,000 or more, about 100,000 or more, or about 200,000 ormore) unique capture probes.

Sequencing the enriched sequencing library generates a plurality ofsequencing reads. In order to determine the sequencing depth for asegment or sub-segment, the number of sequencing reads mapped to thatsegment is determined. Sequencing reads can be mapped, for example, byaligning the sequencing reads (or a portion of the sequencing reads) toa reference sequence, or by assigning the sequencing read to a segmentbased on a portion of the sequencing read.

In some embodiments, the sequencing reads are mapped by aligning thesequencing reads (or a portion of the sequencing reads) to a referencesequence. For example, sequencing reads resulting from direct targetedsequencing can include a capture probe portion (that is, the portion ofthe sequencing read that is attributable to the capture probe itself)and a segment portion (that is, the portion of the sequencing read thatis attributable to the segment targeted by and associated with thecapture probe). In some embodiments, the segment portion is aligned withthe reference sequence, the capture probe portion is aligned with thereference sequence, or the capture probe portion and the segment portionare aligned with the reference sequence. The reference sequence includesthe region of interest pre-dived into segments. Therefore, thesequencing reads aligned to the reference sequence can be aligned to acorresponding segment, and the aligned sequencing reads are assigned or“mapped” to that segment.

In some embodiments, the sequencing reads are mapped by assigning thesequencing read to a segment based on a portion of the sequencing read.In such an embodiment, it is not necessary to align the sequencing readto a reference sequence. Because the capture probes each correspond witha segment, and the corresponding segment is known by the design of thecapture probe, sequencing reads that contain a sequence of the captureprobe (or its complement) can be assigned (or “mapped”) to thecorresponding segment.

In some embodiments, the sequencing depth may be obtained by determiningthe sequencing reads mapped to that segment. In some embodiments thesequencing depth may be obtained by determining the sequencing readsmapped to a capture probe corresponding to that segment.

In some embodiments, two or more capture probes overlap (that is, thecapture probes can hybridize to overlapping sequences within the regionof interest). The two or more capture probes may overlap by about0%-10%, about 10-20%, about 20%-30%, about 30%-40%, about 40%-50%, about50%-60%, about 60%-70%, about 70%-80%, about 80%-90%, or about 90%-99%of the length of the probe. In some embodiments, two or more captureprobes overlap 100%. In some embodiments, the number of sequencingattributable to two or more capture probes correlate with each other.Overlapping or correlated capture probes can be accounted for by merging(i.e., adding together) the number of sequencing reads attributed to theoverlapping or correlated capture probes.

Once the plurality of sequencing reads are mapped to the interrogatedsegment or a plurality of spatially adjacent segments (including theinterrogated segment), the number of sequencing reads mapped to theinterrogated segment or the spatially adjacent segments (including theinterrogated segment) can be determined by counting the number ofsequencing reads that have been assigned to the segment.

Building, Initializing and Maximizing a Copy Number Likelihood Model

The copy number likelihood model may be any statistical model that canbe used to determine the likelihood of observing a number of sequencingreads mapped at a segment given the copy number state of the segment. Aninitial copy number likelihood model refers to the model where theparameters for the model have been defined, but before optimizing it. Ina preferred embodiment the copy number likelihood model includes one ormore likelihood distributions for an expected number of mappedsequencing reads given a copy number state. That is, each likelihooddistribution corresponds to a copy number state. For example the copynumber likelihood model may comprise a likelihood distribution of anexpected number of sequencing reads given a copy number state of 1, alikelihood distribution of an expected number of sequencing reads givena copy number state of 2, a likelihood distribution of an expectednumber of sequencing reads given a copy number state of 3, and alikelihood distribution of an expected number of sequencing reads givena copy number state of 4. The copy number likelihood model need notcomprise a likelihood distribution for each possible copy number state,but comprises at least one likelihood distribution. Similarly, the copynumber likelihood model may comprise distributions for copy numberstates greater than 4, such as a copy number state of 5, of 6, of 7 orof 8. In some embodiments the distributions comprised in the copy numberlikelihood model are Poison distributions. In some embodiments thedistributions comprised in the copy number likelihood model are binomialdistributions. In some embodiments the copy number likelihood modelcomprises negative binomial distributions. For example, in someembodiments the copy number likelihood model comprises one or morenegative binomial distributions (or one or more negative binomialdistributions, wherein the negative binomial distribution is not aPoisson distribution) for expected mapped sequencing reads forinterrogated segment i in test sequencing library j for copy numberstates c_(i,j).

The likelihood distribution of the copy number likelihood model can befurther characterized by a mean (μ) and a dispersion (d). The mean andthe dispersion of the likelihood distribution are optimized by using adetermined expected number of sequencing reads, at segment i (that is,using the same capture probe) by sequencing the test sequencing libraryj at a plurality of segments (that is, using a capture probe library)and by setting a copy number state at the segment i for sequencinglibrary j. The expected number of sequencing reads is based on at leastthree factors: the average number of mapped sequencing reads for thesegment across a plurality of sequencing libraries, the average numberof mapped sequencing reads for the test sequencing library across aplurality of segments, and the local copy number state of the segment.The mean of the distribution can be set as: μ=c_(i,j)μ_(i)μ_(j) whereinμ_(i) is the average number of mapped sequencing reads for segment iacross N_(s) sequencing libraries, μ_(j) is the average number of mappedsequencing reads for the test sequencing library j across N_(p)segments, and c_(i,j) is the copy number state at segment i for testsequencing library j and k_(i,j) is the determined number of sequencingreads at segment i for test sequencing library j.

Formally:

$\mu_{i} = \frac{\sum_{j}k_{i,j}}{N_{s}}$$\mu_{j} = \frac{\sum_{i}{k_{i,j}/\mu_{i}}}{N_{p}}$

The copy number likelihood model is set by determining distributionsfrom an expected number of sequencing reads for different copy numberstates then maximized for a most probable c_(i,j) given the number ofactual mapped sequencing reads at the segment.

For the majority of genes the expected copy number (i.e., “wild-type”)is assumed to be two (i.e., diploid). This is not necessarily always thecase. For example, for genes on the Y chromosome the expected copynumber (i.e., “wild-type”) should be assumed to be 1. Considering thisrelationship, in some embodiments the copy number likelihooddistribution for any given copy number state is centered at an average

$\mu_{c,i,j} = {\frac{c}{2}\mu_{i}\mu_{j}}$

wherein μ_(i) is the average number of mapped sequencing reads forsegment i across N_(s) sequencing libraries, μ_(j) is the average numberof mapped sequencing reads for the test sequencing library j acrossN_(p) segments, and c is the number of copies for the given copy numberlikelihood distribution, wherein μ_(i) is a normalized average number ofmapped sequencing reads. The number of mapped sequencing reads forsegment i in a given sequencing library can be normalized by dividingthe number of mapped sequencing reads at segment i within the sequencinglibrary by the average number of mapped sequencing reads across N_(p)segments within that sequencing library. FIG. 2A presents an exampleprofile of the number of sequencing reads for approximately 2500 captureprobes, wherein the sequencing library was enriched by direct targetedsequencing. FIG. 2B present an example profile of a normalized number ofmapped sequencing reads at segment i for approximately 48 differentsequencing libraries, wherein the sequencing library was enriched forsegment i by direct targeted sequencing.

The copy number likelihood distribution also includes a dispersion (d,estimated for segment i as:

$d_{i} = \frac{\mu_{i}^{2}}{\sigma_{i}^{2} - \mu_{i}}$

wherein σ_(i) ² is the variance of the number of mapped sequencing readsfor the plurality of sequencing libraries.

The copy number likelihood distribution can be a Poisson distribution, abinomial distribution, a negative binomial distribution (such as ageneralized Poisson negative binomial distribution or a negativebinomial distribution the is not a Poisson distribution), or any othersuitable distribution. It has been found that a negative binomialdistribution, wherein the negative binomial distribution is not aPoisson distribution is particularly useful for determining the copynumber likelihood distributions. FIG. 3A shows a plot of the sequencingdepth variance against the mean number of sequencing reads (“meandepth”) for approximately 2500 capture probes used to enrich asequencing library for a region of interest for a plurality of differenttest sequencing libraries. The data was fit using a negative binomialdistribution, wherein the negative binomial distribution is not aPoisson distribution. As a comparison, a Poisson distribution is alsoillustrated, which assumes a linear relationship between dispersion andmean depth. As it can be seen in FIG. 3A, the data violates the Poissonassumption that the mean sequencing depth is equal to the sequencingdepth variance, as plotting the data shows that variance is greater thanmean. Thus, the data fits a negative binomial distribution significantlybetter than the Poisson distribution.

FIG. 3B illustrates a copy number likelihood model including a copynumber likelihood distribution for a copy number of 1 (CN=1), 2 (CN=2),and 3 (CN=3). FIG. 3B illustrates a Poisson distribution and a negativebinomial distribution, wherein the negative binomial distribution is nota Poisson distribution. for each copy number. The distributions areprobability mass functions (pmf) as a function of the number ofsequencing reads from the capture probe corresponding with the segment.

Building a Hidden Markov Model

A hidden Markov model allows for the determination of a most probablecopy number (a hidden state) from the number of mapped sequencing reads(an observation state). Generally, there are four main parameters in thehidden Markov model: one or more hidden states, one or more observationstates, one or more emission probabilities from the hidden states to theobservation states, and the transition probabilities between the hiddenstates. Provided herein are methods of building the hidden Markov modeland parameterizing the hidden Markov model. Also, provided herein aremethods of training the hidden Markov model using an incomplete dataset. Also provided herein are methods of optimizing the hidden Markovmodel by optimizing parameters in the hidden Markov model to account forvariables that affect the emission probabilities between the hiddenstates and the observation states. Specifically, provided below aremethods and explanations on the layers of the hidden Markov model; thetransition probabilities of the Markov model; the copy number likelihoodmodel; using expectation-maximization to parameterize the hidden Markovmodel; adjusting the hidden Markov model to account for a number oflatent variables; solving the hidden Markov model.

An exemplary hidden Markov model that can be used with the disclosedmethods is illustrated in FIG. 4A. In FIG. 4A, c₁, c₂, c₃, and c₄represent the hidden states (i.e., the most probable copy number forfour different segments, although it is understood that the model caninclude n number of segments) and k₁, k₂, k₃, and k₄ represent theobserved states (i.e., the number of mapped sequencing reads for eachcorresponding segment). The transition probabilities are the probabilityof transitioning from a copy number for one segment to a copy number inan adjacent segment, and is represented by p(c₂|c₁), p(c₃|c₂), andp(c₄|c₃). Finally, the probability of a hidden state (i.e., the copynumber for the segment) given the observed state (the number of mappedsequencing reads for that segment) is represented by p(c₁|k₁), p(c₂|k₂),p(c₂|k₂), and p(c₂|k₂). The latter is the posterior probability that issolved for. To determine the posterior probability, the copy numberlikelihood model of p(k₁|c_(n)) is used.

In some embodiments a hidden Markov model comprises only one hiddenstate and a corresponding observation state. In some embodiments thehidden state corresponds to the copy number state of a segment and theobservation state corresponds to the mapped number of sequencing readsat that segment. In some embodiments the hidden Markov model comprises aplurality of hidden states and a plurality of observation states. Insome embodiments the plurality of the hidden states corresponds to thecopy number states at a plurality of segments and the plurality ofobservation states corresponds to the number of mapped sequence reads atthe plurality of segments. In some embodiments, each segment within aregion of interest corresponds to a capture probe for the region ofinterest. In some embodiments, two adjacent hidden states correspond totwo spatially adjacent segments within the region of interest.

The segments may be divided in sub-segments, as previously describedherein. In some embodiments the hidden states correspond to the copynumber of the sub-segments. The sub-segments do not include a mappednumber of sequencing reads independent of the mapped number ofsequencing reads for the parent segment (that is, the segment to whichthe sub-segment is a member). In some embodiments, the mapped number ofsequencing reads for the segment is attributed to each sub-segmentwithin the segment. In some embodiments, the sub-segment includes ahidden state (i.e., a copy number), but the mapped number of sequencingreads is only attributed to the first sub-segment of the segment. Thisis illustrated in FIG. 3B. FIG. 4B includes two segments identified bythe dashed lines: Segment A and Segment B. Segment A includessub-segment 1, sub-segment 2, and sub-segment 3, while Segment Bincludes sub-segment 4, sub-segment 5, and sub-segment 6. The number ofmapped sequencing reads for Segment A is attributed to the firstsub-segment in that segment, sub-segment 1. The number of mappedsequencing reads for Segment B is attributed to the first sub-segment inthat segment, sub-segment 4. C₁, C₂, C₃, C₄, C₅, and C₆ represent thehidden state (copy number) for each of the sub-segments, and K₁ and K₄represent the observed states (number of sequencing reads) forsub-segment 1 and sub-segment 4, respectively. The transitionprobabilities between the sub-segment hidden states are identified byp(c₂|c₁), p(c₃|c₂), p(c₄|c₃), p(c₅|c₄) and p(c₆|c₅). Because onlysub-segment 1 and sub-segment 4 include observation states, only twoprobabilities for a number of mapped sequencing reads given a copynumber of the sub-segment are included: p(k₁|c₁) and p(k₄|c₄).

The copy number state of a segment is related to the number ofsequencing reads mapped to that location. Determining a copy numberstate of a segment or sub-segment (which can be denoted as c_(i,j))given a number of mapped sequencing reads (which can be denoted ask_(i,j)) for segment (or sub-segment) i in test sequencing library jallows for calling of a copy number of that segment or sub-segment. Theprobability for a given copy number state being the correct copy numberdepends at least on the number of mapped sequencing reads. In Bayesianstatistics, the posterior probability of c_(i,j) given k_(i,j) (that is,p(c_(i,j)|k_(i,j))) can be determined using a copy number likelihooddistribution. While posterior probability is a probability of aparameter given some data; a likelihood model is the probability of thedata, given the parameter. In this case, the posterior probability isthe probability of the copy number state of a segment or sub-segmentgiven the number of sequencing reads mapped at that segment orsub-segment (that is, p(c_(i,j)|k_(i,j))), whereas the copy numberlikelihood model is the likelihood of observing a number of sequencingreads mapped at a segment given the copy number state of the segment(that is, p(k_(i,j)|c_(i,j))). Since p(c_(i,j)|k_(i,j)) cannot bedirectly determined, the copy number likelihood model p(k_(i,j)|c_(i,j))can be used to parameterize the hidden Markov model, which can be usedto solve for the posterior probability p(c_(i,j)|k_(i,j)). The followingdiscusses the copy number likelihood model as a negative binomialdistribution, but it is understood that the similar aspects would applyfor other distribution forms. In some embodiments, the copy numberlikelihood model can be defined as:

p(k _(i,j) |c _(i,j))=NegBinom(k _(i,j)|μ_(c,i,j) =c _(i,j)μ_(i)μ_(j) ;d=d _(i))

wherein k_(i,j) is the number of mapped sequencing reads at segment ifor the test sequencing library/

The negative binomial distribution is parameterized to best fit thedata. In its simplest form the copy number likelihood model is anegative binomial model. However, depending on the data generated, adifferent type of distribution may fit the data better and may be bettersuited. The general aspects of this invention would apply to modelscomprising different statistical distributions.

The transition probability for a copy number of a segment or sub-segmentdepends, in part, on the copy number state of a spatially adjacentsegment or sub-segment. Lengths and frequencies of copy number variantscan also impact the transition probabilities.

In some embodiments, the transition probability can be predetermined orfixed. In a preferred embodiment, the transition probability isvariable. For example, the transition probability can be formallyrepresented by the following stochastic transition matrix assuming ahidden copy number state limited to 0, 1, 2, 3, or 4 copies (assuming awildtype copy number of 2):

${p\left( C_{i + 1} \middle| C_{i} \right)} = \begin{bmatrix}{1 - r_{01}} & r_{10} & 0 & 0 & 0 \\r_{01} & {1 - r_{12} - r_{10}} & r_{21} & 0 & 0 \\0 & r_{12} & {1 - r_{23} - r_{21}} & r_{32} & 0 \\0 & 0 & r_{23} & {1 - r_{32} - r_{34}} & r_{43} \\0 & 0 & 0 & r_{34} & {1 - r_{43}}\end{bmatrix}$

wherein C_(i) is the copy number state of a first segment or firstsub-segment; C_(i+1) is the copy number state of the second segment orsecond sub-segment that is spatially adjacent to the first segment orfirst sub-segment; and r_(ab) represents the transition probability froma first copy number state a to a second copy number state b. Forexample, a can be a copy number state of 3 and b can be a copy numberstate of 2. The first segment can be the interrogated segment (or thefirst sub-segment can be a sub-segment of the interrogated segment).Although the above stochastic transition matrix assumed 0, 1, 2, 3, or 4copies, it is understood that a stochastic transition matrix can be usedfor any number of copies.

Copy number variants have an average length, and copy numbers that arelonger or shorter than this length are less likely than copy numbers atthe average length. In some embodiments the transition probability (ortransition probabilities) account for an average length of a copy numbervariant. The average length of the copy number variant can be based onobservations from a historical population (e.g., a historical humanpopulation). The historical population is a historical population ofsequencing libraries for which a copy number variant has been called.Larger historical populations can result in more accurate average copynumber variant lengths. In some embodiments, the historical populationcomprises about 1000 or more sequencing libraries (such as about 5000 ormore, about 10,000 or more, about 25,000 or more, about 50,000 or more,about 100,000 or more, about 250,000 or more, or about 500,000 or moresequencing libraries). The average length of a copy number variant ispredetermined. In some embodiments, the average length of a copy numbervariant is about 3000 to about 1000 bases (such as about 4000 to about8000 bases, about 5000 to about 7000 bases, about 5500 bases to about6500 bases, or about 6200 bases). Accounting for the average length of acopy number, the transitions in the stochastic transition matrix whichis used to calculate the per base transition probability (or sub-segmenttransition probability can be set as:

$r_{01} = {r_{12} = {r_{32} = {r_{43} = \frac{1}{\left\langle l \right\rangle_{CNV}}}}}$

wherein <l>_(CNV) is the average length of a copy number variant.

The transition probabilities can also account for the probability of acopy number variant at the interrogated segment given the copy numberstate at a spatially adjacent segment. Certain portions of the genomemay include “hot spots” of genetic variation, including copy numbervariation. Hot spots, refers to regions in the genome which display ahigh propensity for mutations of all kinds. This might be due tostructural makeup of the region, or functional aspects of the region,which make it more prone to mutations. The probability of a copy numbervariant at any given segment (such as an interrogated segment or aspatially adjacent segment) can be based on observations from ahistorical population (e.g., a historical human population). Thehistorical population is a historical population of sequencing librariesfor which a copy number variant has been called. Larger historicalpopulations can result in more accurate copy number variantprobabilities. In some embodiments, the historical population comprisesabout 1000 or more sequencing libraries (such as about 5000 or more,about 10,000 or more, about 25,000 or more, about 50,000 or more, about100,000 or more, about 250,000 or more, or about 500,000 or moresequencing libraries). To account for the probability of a copy numbervariant at the interrogated segment or a spatially adjacent segment, thetransitions in the stochastic transition matrix can be set as:

$r_{21} = {r_{12}\frac{p_{CNV}}{1 - {2p_{CNV}} - {2p_{CNV}^{2}}}}$

wherein p_(CNV) is the probability of a copy number variant. Sincer₀₁=r₁₂=r₃₂=r₄₃ the relationship described holds true for all copynumbers.

In some embodiments, the hidden Markov model comprises one transitionprobability of a copy number state of a segment or of a sub-segment. Insome embodiments, the hidden Markov model comprises a plurality oftransition probabilities of a copy number state of a segment or of asub-segment. In some embodiments, the transition probability of a copynumber state given the copy number state of an adjacent precedingsegment is dependent on length of a copy number variant. In someembodiments, the length of the copy number variant is specific for thatparticular region of the genome. In some embodiments, the length of acopy number variant is the average length of a copy number variantacross the genome.

In some embodiments the transition probability of a copy number stategiven the copy number state of an adjacent preceding segment isdependent on the probability of observing a copy number variant. In someembodiments the probability of observing a copy number variant isspecific for that particular region of the genome. In some embodimentsthe probability of observing a copy number variant is the averageprobability of observing a copy number variant across the genome.

Parameterizing the Hidden Markov Model and Determining a Most ProbableCopy Number

As described above, the hidden Markov model includes (i) one or morehidden states comprising a copy number corresponding to the one or moresegments or sub-segments (including at least the interrogated segment ora sub-segment of the interrogated segment), (ii) one or more observationstates comprising the number of sequencing reads mapped to the one ormore segments, and (iii) the copy number likelihood model. The copynumber likelihood model is used to describe the probability of observingan observation state for a given hidden state (that is,p(k_(ij)|c_(i,j))). The hidden Markov model also includes a transitionprobability between the hidden states, which can be fixed or variable asdescribed above.

The hidden Markov model is initiated using the copy number likelihoodmodel. The hidden Markov model can also be initiated by assuming thecopy number state (i.e., the hidden state) to have a wild-type number ofcopies (for example, two copies), which can be used to back-calculatethe transitions (r) for determining the transition probabilities. Thecopy number likelihood model is based on the expected number ofsequencing reads mapped to the segment, as explained above, but the copynumber likelihood model can be adjusted to fit the determined number ofsequencing reads mapped to the segment (i.e., the observed states), forexample by allowing the mean μ_(c,i,j) and dispersion d_(i) for eachcopy number likelihood distribution in the copy number likelihood modelto float when parameterizing the hidden Markov model. The transitionprobabilities, if variable, can also be adjusted during parameterizationof the hidden Markov model.

Parameterization of the hidden Markov model includes adjusting the copynumber likelihood model to fit the determined number of sequencing readsmapped to the segment (e.g., the interrogated segment or the spatiallyadjacent segments). In some embodiments, the copy number likelihoodmodel is optimized to fit the determined number of sequencing readsmapped to the segment (e.g., the interrogated segment or the spatiallyadjacent segments). The copy number likelihood model is “optimized”after a plurality of adjustment rounds to best fit the observed states.In some embodiments, parameterization of the hidden Markov modelincludes adjusting (or optimizing) the transition probabilities. Thehidden Markov model can be optimized by a collection of usefulalgorithms known in in the art, such as the class ofExpectation-Maximization (EM) algorithms (including the Baum-Welchalgorithm, which includes alpha-beta recursion), a Viterbi algorithm, aQuasi-Newton solver, or a Markov chain Monte Carlo.

For example, expectation-maximization (EM) may be used to adjust (oroptimize) the copy number likelihood model (based on the expected numberof sequencing reads) to find a maximized expected sequencing readsmapped to the segment (that is, an adjusted μ_(c,i,j)) and an adjusteddispersion for that segment (that is, an adjusted d_(i)). That is, sothat the probability of an expected number of sequencing reads at aninterrogated segment is maximized for a given copy number state at thatsegment.

Generally, expectation-maximization (EM) can be used to estimate latent,or unknown parameters despite incomplete data. The EM algorithm caniteratively alternate between the expectation “E” step which selects amost likely copy number likelihood distribution from the copy numberlikelihood model given the determined number of sequencing reads mappedto the segment (such that the most probable copy number can bedetermined), and a maximization “M” step, which re-estimates the copynumber likelihood model parameters (i.e., μ_(c,i,j) and d_(i)). TheMaximization step assumes a fixed probabilistic model and number ofsequencing reads, and then finds the copy number state that would, whenapplied to the model, result into a highest probability for the actualnumber of mapped sequencing reads out of all other possible copynumbers. An EM process can be applied at different parameters of theHMM, for example it can consider the transitions (r) between the hiddenstates if applicable, using the expectations generated in the “E” step.Simplistically, the EM is used to maximize the model so that we find forwhich c_(i,j) are we most likely to see the number of mapped sequencingreads that we observed. Formally, a Vitterbi algorithm can determine themaximum likelihood for the copy number likelihood model as:

$c_{i,j}^{*} = {\arg{\max\limits_{c_{i,j}}{p\left( k_{i,j} \middle| c_{i,j} \right)}}}$

In some embodiments, a Baum-Welch algorithm is used to parameterize thehidden Markov model. The Baum-Welch algorithm uses a posteriorprobability α(c_(i)|k_([0,i])), which is the probability of a copynumber state at segment i for a given number of mapped sequencing readsat segment i, and a likelihood β(k_([i,I])|c_(i)), which is theprobability of the number of mapped sequencing reads for the downstreamspatially adjacent segments i to I for a given copy number state atsegment i. The Baum-Welch algorithm can be solved using methods known bya person of skill in the art.

The parameterized hidden Markov model can be used to determine a mostprobable copy number of the interrogated segment or a sub-segment of theinterrogated segment during the Maximization step. The most probablecopy number of the interrogated segment can be determined using anyuseful algorithm known in the art, such as a Viterbi algorithm, aQuasi-Newton solver, or a Markov chain Monte Carlo.

GC Content Bias Correction

GC content of a segment of the region of interest or a capture probecorresponding to the segment can affect the number of sequencing readsmapped to the segment, for example due to differences in hybridizationefficiency of the capture probe. Thus, depending on GC content, acapture probe may have strong effects on the number of sequencing readsmapped to a segment, irrespective of the copy number state at thatsegment. This GC content bias is well known and described in the art. Insome embodiments of the methods described herein, the GC content bias isaccounted for when determining a copy number of the segment. The GCcontent bias correction can be useful in any method of determining acopy number variant, and need not be used solely with direct targetedsequencing. For example, in some embodiments, GC content bias iscorrected when determining a copy number of a segment in a region ofinterest, wherein the sequencing library is enriched using hybridcapture techniques. Additionally, the methods for correcting GC contentbias need not be limited to methods using a hidden Markov model todetermine a copy number, but the GC content bias can be corrected forany method that includes the use of a copy number likelihood model.

In some embodiments, a number of sequencing reads (such as the expectednumber of sequencing reads used to determine the copy number likelihoodmodel) for any given segment is corrected for GC content by multiplyingthe number of sequencing reads by a GC bias correction factor. The GCbias correction factor is specific for the given segment and for thetest sequencing library. That is, the GC bias correction factor isuniquely determined for the segment and the test sequencing library, andthe GC bias correction factor must be re-determined for a differentsegment and for each different test sequencing library.

The number of sequencing reads mapped to a given segment (which mayinclude the interrogated segments) can be normalized by dividing thenumber of mapped sequencing at that segment by the average number ofmapped sequencing reads for a plurality of segments enriched from thetest sequencing library. The normalized number of sequencing reads foreach segment within the plurality of segments can be plotted against theGC content at that segment. The data points can then be fit using asecond order correction:

k _(N,J) =a+b(GC)+c(GC)²

wherein k_(N,j) is the normalized number of sequencing reads specificfor test sequencing library j for the plurality of segments, (GC) is theGC content, and a, b, and c are constants determined by the second orderfit.

The GC bias correction factor can therefore be determined by fitting asecond order function to a plurality of data points, wherein the datapoints each comprises a normalized number of sequencing reads mapped toa segment and the GC content of that segment, and wherein the pluralityof data points represent a plurality of segments enriched by the captureprobes in the test sequencing library; and defining the GC biascorrection factor to be the normalized number of sequencing readsdetermined by the second order function for the GC content of thesegment.

The copy number likelihood model can be adjusted to account for thepresence of GC content bias in a similar manner. That is, the expectednumber of sequencing reads used as a basis for the copy numberlikelihood model can be adjusted to account for the presence of GCcontent. For example, the average of the copy number likelihooddistribution in the model can be adjusted such that:

μ_(c,i,j) =c _(i,j)μ_(i)μ_(j) k _(i,j)

Further, the copy number likelihood model can be formalized as:

p(k _(i,j) |c _(i,j))=NegBinom(k _(i,j)|μ_(c,i,j) =c _(i,j)μ_(i)μ_(j) k_(i,j) , d=d _(i))

In some embodiments, there is a method for determining a copy number ofan interrogated segment or a sub-segment of the interrogated segmentwithin a region of interest comprising: (a) mapping a plurality ofsequencing reads generated from a test sequencing library to a segmentwithin a region of interest, wherein the test sequencing library isenriched using a capture probe; (b) determining a number of sequencingreads mapped to the segment; (c) determining a copy number likelihoodmodel for the segment based on an expected number of mapped sequencingreads at the segment, wherein the expected number of mapped sequencingreads is corrected for GC content of the segment; and (d) determining amost probable copy number of the interrogated segment based on the copynumber likelihood model. The most probable copy number of theinterrogated segment can be determined based on the copy numberlikelihood model using the hidden Markov model described herein, or canbe done by any other method known in the art. For example, the mostprobable copy number can be determined based on the maximum copy numberprobability of each region based on a capture probe for that region. Inanother example, the most probable copy number can be determined using abrute force segmentation approach.

In some embodiments, there is a method for determining a copy number ofan interrogated segment or a sub-segment of the interrogated segmentwithin a region of interest comprising: (a) mapping a plurality ofsequencing reads generated from a test sequencing library to theinterrogated segment, wherein the test sequencing library is enrichedusing one or more capture probes; (b) determining a number of sequencingreads mapped to the interrogated segment; (c) determining a copy numberlikelihood model based on an expected number of sequencing reads mappedto the interrogated segment, wherein the expected number of mappedsequencing reads is corrected for GC content of the interrogatedsegment; (d) building a hidden Markov model comprising: (i) one or morehidden states comprising a copy number corresponding to the interrogatedsegment or a plurality of sub-segments within the interrogated segment,(ii) an observation state comprising the number of sequencing readsmapped to the interrogated segment; and (iii) the copy number likelihoodmodel; (e) parameterizing the hidden Markov model by adjusting the copynumber likelihood model to fit the determined number of sequencing readsmapped to the interrogated segment; and (f) determining a most probablecopy number of the interrogated segment or a sub-segment of theinterrogated segment based on the parameterized hidden Markov model.

In some embodiments there is a method for determining a copy number ofan interrogated segment or a sub-segment of the interrogated segmentwithin a region of interest comprising: (a) mapping a plurality ofsequencing reads generated from a test sequencing library to a pluralityof spatially adjacent segments, wherein the plurality of spatiallyadjacent segments comprises the interrogated segment, and wherein thetest sequencing library is enriched using a plurality of spatiallyadjacent capture probes; (b) determining a number of sequencing readsmapped to each spatially adjacent segment; (c) determining a copy numberlikelihood model for each spatially adjacent segment based on anexpected number of mapped sequencing reads at the spatially adjacentsegment, wherein the expected number of mapped sequencing reads iscorrected for GC content of the spatially adjacent segment; (d) buildinga hidden Markov model comprising: (i) a plurality of hidden statescomprising a copy number for each of the spatially adjacent segments ora plurality of sub-segments within each of the spatially adjacentsegments, (ii) a plurality of observation states comprising the numberof sequencing reads mapped to each spatially adjacent segment, and (iii)the copy number likelihood model for each spatially adjacent segment;(e) parameterizing the hidden Markov model comprising adjusting eachcopy number likelihood model to fit the determined number of sequencingreads mapped to each spatially adjacent segment; and (f) determining amost probable copy number of the interrogated segment or a sub-segmentof the interrogated segment based on the parameterized hidden Markovmodel.

Spurious Capture Probes

Certain capture probes used to enrich a segment within the region ofinterest can produce spurious results. For example, the number ofsequencing reads generated by a spurious capture probe may not beconsistent with the copy number of a corresponding segment, either byunder or over enriching the segment. These spurious results can occur,for example, due to capture probe design or sequence variants (e.g.,SNPs) within the sequence the capture probe was designed to hybridizeto. Spurious capture probes affect number of mapped sequencing reads andcan artificially confound the copy number likelihood model andparameters. It is therefore desirable to account for spurious captureprobes. Spurious capture probes need not be direct targeted sequencingcapture probes, and similar methods can be applied to capture probesused to enrich a test sequencing library (such as by hybrid capturetechniques). The determination of whether a capture probe is a spuriouscapture probe can be made using EM. For example, the determination ofwhether the capture probe is spurious can be made during the expectationstep, and when the probability of a capture probe being spurious changesduring EM iterations, so will the maximization step, which in turndetermines the most likely copy number state of the segment which nowtakes into consideration the spuriosity of the capture probe. If acapture probe is determined to be a spurious capture probe, theprobability of the number of mapped sequencing reads for a segment for acopy number state is set to 1 during the expectation-maximizationprocess. By setting it a constant it effectively allows the model todisregard the spurious capture probe as it provides no additionalinformation and is thus not taken into consideration as the model isparameterized. Determination of the spuriousness of the capture probecan be iterative, for example by determining whether the capture probeis spurious after a number of EM cycles.

In some embodiments a Bernoulli process is used to determine theprobability that a given capture probe is spurious. The Bernoulliprocess can be applied to some or all of the capture probes. That is,for each capture probe its spuriosity is independently determined. Forcapture probe i, an indicator variable b_(i) is introduced where 1 meansthat the capture probe t is spurious and 0 means that the capture probeis not spurious.

b_(i)∈{0,1}

By using this indicator, it is possible to account for spurious captureprobes by adjusting the copy number likelihood model. If a capture probeis determined to be spurious, the probability of a number of mappedsequencing reads for the corresponding segment for any given copy numberis set to 1. If the capture probe is non-spurious, the copy numberlikelihood distributions in the copy number likelihood model areunchanged. Formally:

${p\left( {\left. k_{i,j} \middle| c_{i,j} \right.,b_{i}} \right)} = \left\{ \begin{matrix}1 & {{{if}\mspace{14mu} b_{i}} = 1} \\{{NegBinom}\left( {\left. k_{i,j} \middle| c_{i,j} \right.;\mu_{c,i,j};d_{i}} \right)} & {{{if}\mspace{14mu} b_{i}} = 0}\end{matrix} \right.$

The indicator on the observed states of the hidden Markov model isillustrated in FIG. 5A.

The spuriousness of capture probes may depend on the test sequencinglibrary. That is, some test sequencing libraries may be more prone tospurious capture probes than other test sequencing libraries. In someembodiments whether a test sequencing library is prone to spuriouscapture probes is determined based on test sequencing library priors. Insome embodiments determining whether a test sequencing library will beprone to a particular probe being spurious depends on a general prior.

FIG. 5B illustrates priors that can be adjusted to determine if a givencapture probe is a spurious capture probe. The indicator variableb_(i,j) is a Bernoulli distribution prior on k_(i), the observationstate (the number of mapped sequencing reads) of segment i. Theindicator variable b_(i,j) may be specific for the segment i and fortest sequencing library j. A test sequencing library prior π_(j) is seton the indicator variable b_(t), and is the same across all segmentswithin the region of interest of the test sequencing library. A generalprior Π is set on the test sequencing library prior π_(j), and is thesame for all sequencing libraries similarly enriched. The general priorII can be pre-determined, and validated to reduce false calls withoutlosing sensitivity. An adjustment step (such as a maximization step inan EM algorithm) can be set up by assuming that the capture probefollows a Bernoulli distribution with a probability of being spurious.The probability of a capture probe i for test sequencing library j beingspurious given the prior π_(j) can be written as:

p(b _(i)|π_(j))=π_(j) ^(b) ^(i) (1−π_(j))^(1−b) ^(i)

As the Bernoulli distribution limits b_(i) to be either 0 or 1, theabove probability is set to π_(j) (when b_(i)=1), or 1−π_(i) (whenb_(i)=0).

Given the determined number of sequencing reads mapped to spatiallyadjacent segments (or spatially adjacent sub-segments) 0 to I, theprobability of capture probe i being spurious can be derived to:

${p\left( b_{i} \middle| k_{\lbrack{0,1}\rbrack} \right)} = \frac{1}{1 + {\sum_{x \in {\lbrack{0,C}\rbrack}}{{NegBinom}\left( k_{i} \middle| c_{i} \right)}}}$

Given the expectation of the indicator b_(i), the test sequencinglibrary prior π_(j) can be determined as:

π_(j)=Π

b _(i)

_(k) _([0,I]) −1

In some embodiments, the most probable copy number of the interrogatedsegment or the one or more sub-segments of the interrogated segment isnot called if the capture probe associated with the interrogated segmentis determined to be spurious. In some embodiments, the most probablecopy number of the interrogated segment or the one or more sub-segmentsof the interrogated segment is not called if the probability of acapture probe i being spurious (that is, p(b_(i)|k_([0,1])) is above apredetermined threshold (such as about 0.1 or more, about 0.2 or more,about 0.3 or more, about 0.4 or more, or about 0.5 or more).

In some embodiments, there is a method for determining a copy number ofan interrogated segment or a sub-segment of the interrogated segmentwithin a region of interest comprising: (a) mapping a plurality ofsequencing reads generated from a test sequencing library to theinterrogated segment, wherein the test sequencing library is enrichedusing one or more capture probes; (b) determining a number of sequencingreads mapped to the interrogated segment; (c) determining a copy numberlikelihood model based on an expected number of sequencing reads mappedto the interrogated segment; (d) building a hidden Markov modelcomprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterizing the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogated segmentand accounting for one or more spurious capture probes; and (f)determining a most probable copy number of the interrogated segment or asub-segment of the interrogated segment based on the parameterizedhidden Markov model.

In some embodiments, there is a method for determining a copy number ofan interrogated segment or a sub-segment of the interrogated segmentwithin a region of interest comprising: (a) mapping a plurality ofsequencing reads generated from a test sequencing library to a pluralityof spatially adjacent segments, wherein the plurality of spatiallyadjacent segments comprises the interrogated segment, and wherein thetest sequencing library is enriched using a plurality of spatiallyadjacent direct targeted sequencing capture probes; (b) determining anumber of sequencing reads mapped to each spatially adjacent segment;(c) determining a copy number likelihood model for each spatiallyadjacent segment based on an expected number of mapped sequencing readsat the spatially adjacent segment; (d) building a hidden Markov modelcomprising: (i) a plurality of hidden states comprising a copy numberfor each of the spatially adjacent segments or a plurality ofsub-segments within each of the spatially adjacent segments, (ii) aplurality of observation states comprising the number of sequencingreads mapped to each spatially adjacent segment, and (iii) the copynumber likelihood model for each spatially adjacent segment; (e)parameterizing the hidden Markov model comprising adjusting each copynumber likelihood model to fit the determined number of sequencing readsmapped to each spatially adjacent segment and accounting for one or morespurious capture probes; and (f) determining a most probable copy numberof the interrogated segment or a sub-segment of the interrogated segmentbased on the parameterized hidden Markov model.

Noisy Test Sequencing Library

During preparation of test sequencing libraries, several steps canresult in the nucleic acid of the test sequencing library to be moreprone to “noise” across multiple capture probes. This results ininconsistent data and a high number of false positives FIG. 6A shows anexample of a less noisy test sequencing library and FIG. 6B shows anexample of a noisier test sequencing library, even though the twosequencing libraries were enriched using the same capture probe library.Noise can be introduced, for example, during preparation or sequencingof the test sequencing library, isolation of the nucleic acids from atest sample, storage of the sequencing library, or fragmentation of thenucleic acids isolated from the test sample can compromise the integrityof the oligonucleotide, which in turn can affect how theoligonucleotide.

In some embodiments, parameterizing the hidden Markov model comprisesaccounting for noise in the number of mapped sequencing reads. In someembodiments, accounting for noise in the number of mapped sequencingreads comprises adjusting the copy number likelihood model. For example,parameterizing the hidden Markov model can include anexpectation-maximization step, and accounting for the noise can occurduring the expectation-maximization step.

The dispersion d of the copy number likelihood distribution in the copynumber likelihood model was discussed above. When only the dispersiondue to the capture probe (i.e., at the segment) is considered, d=d_(i).The dispersion of the copy number likelihood distribution can also beused to account for noise across the segments in the test sequencinglibrary j. Thus, the dispersion of the copy number likelihooddistribution can formally be considered as:

d=d _(i) *d _(j)

Parameterization of the hidden Markov model adjusts the copy numberlikelihood model, including the dispersion of the copy number likelihooddistributions with the model. Thus, both components of the dispersion d(that is, d_(i) and d_(j)) can be adjusted during parameterization ofthe hidden Markov model, for example using an expectation maximizationalgorithm. In some embodiments, a quasi-Newton method can be used toaccount for the noise during the maximization step. In particular, theexpectation step asks to maximize the following

$\left\langle {l\left( {\overset{\rightarrow}{\mu},\overset{\rightarrow}{d}} \right)} \right\rangle_{k{\lbrack{0,T}\rbrack}} = {\underset{j \in {{cpt}\mspace{11mu}{probes}}}{\sum\limits_{i \in {TSLs}}^{\;}}{{p\left( {x_{ij} = \left. 2 \middle| {k\left\lbrack {0,T} \right\rbrack} \right.} \right)}{p\left( {b_{ij} = \left. 0 \middle| {k\left\lbrack {0,T} \right\rbrack} \right.} \right)}\mspace{11mu}\ln\mspace{14mu}{{NegBinom}\left( {\left. k_{ij} \middle| x_{i,j} \right.,\overset{\rightarrow}{\mu},\overset{\rightarrow}{d}} \right)}}}$

In the equation, l({right arrow over (μ)}, {right arrow over (d)})represents the expected logarithmic likelihood given all the data andthe current parameters of the model. TSL stands for test sequencinglibrary and cpt probes refers to capture probes. The mean {right arrowover (μ)} can be approximated by using a double normalization, whichaccounts for both the median sequencing depth across segments within atest sequencing library and the median sequencing depth of a pluralityof test sequencing library across the same segment. In some embodiments,to find the dispersion {right arrow over (d)} that can maximize thisfunction a quasi-Newtonian method is used. The quasi-Newton method setsthe partial derivative of this function with respect to {right arrowover (d)} to 0. Since the test sequencing library and the capture probeshape are independent, it is equivalent to setting the partialderivative of each type to 0.

${\frac{\partial\left\langle {l\left( {\overset{\rightarrow}{\mu},\overset{\rightarrow}{d}} \right)} \right\rangle_{k{\lbrack{0,T}\rbrack}}}{\partial\overset{\rightarrow}{d}} = \frac{\partial\left\langle {l\left( {\overset{\rightarrow}{\mu},\overset{\rightarrow}{d}} \right)} \right\rangle_{k{\lbrack{0,T}\rbrack}}}{\partial d_{i}}},\frac{\partial\left\langle {l\left( {\overset{\rightarrow}{\mu},\overset{\rightarrow}{d}} \right)} \right\rangle_{k{\lbrack{0,T}\rbrack}}}{\partial d_{j}}$

Once the parameters of the distribution are set, the parameterizedhidden Markov model can be used to determine the most probable copynumber state of the segment.

Computer Systems

Further contemplated herein are computing system configured to performany one of the processes described herein, including the variousexemplary processes for determining a copy number of an interrogatedsegment or determining a copy number variant abnormality within a regionof interest. In this context, the computing system may include, forexample, a processor, memory, storage, and input/output devices (e.g.,monitor, keyboard, disk drive, Internet connection, etc.). However, thecomputing system may include circuitry or other specialized hardware forcarrying out some or all aspects of the processes. In some operationalsettings, the computing system may be configured as a system thatincludes one or more units, each of which is configured to carry outsome aspects of the processes either in software, hardware, or somecombination thereof.

In some embodiments the computing system includes a number of componentsthat may be used to perform the processes described herein. The systemcan include a motherboard having an input/output (“I/O”) section, one ormore central processing units (“CPU”), and a memory section, which mayhave a flash memory card related to it. The I/O section can be connectedto a display, a keyboard, a disk storage unit, and a media drive unit.The media drive unit can read/write a computer-readable medium, whichcan contain programs (i.e., instructions) and/or data.

At least some values based on the results of the processes describedherein can be saved for subsequent use. Additionally, a non-transitorycomputer-readable medium can be used to store (e.g., tangibly embody)one or more computer programs for performing any one of theabove-described processes by means of a computer. The computer programmay be written, for example, in a general-purpose programming language(e.g., Pascal, C, C++, Java, Python, JSON, etc.) or some specializedapplication-specific language.

EXEMPLARY EMBODIMENTS

Embodiment 1. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to the interrogated segment, wherein the        test sequencing library is enriched using one or more direct        targeted sequencing capture probes;    -   (b) determining a number of sequencing reads mapped to the        interrogated segment;    -   (c) determining a copy number likelihood model based on an        expected number of sequencing reads mapped to the interrogated        segment;    -   (d) building a hidden Markov model comprising:        -   (i) one or more hidden states comprising a copy number            corresponding to the interrogated segment or a plurality of            sub-segments within the interrogated segment,        -   (ii) an observation state comprising the number of            sequencing reads mapped to the interrogated segment; and        -   (iii) the copy number likelihood model;    -   (e) parameterizing the hidden Markov model by adjusting the copy        number likelihood model to fit the determined number of        sequencing reads mapped to the interrogated segment; and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 2. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to a plurality of spatially adjacent        segments, wherein the plurality of spatially adjacent segments        comprises the interrogated segment, and wherein the test        sequencing library is enriched using a plurality of spatially        adjacent direct targeted sequencing capture probes;    -   (b) determining a number of sequencing reads mapped to each        spatially adjacent segment;    -   (c) determining a copy number likelihood model for each        spatially adjacent segment based on an expected number of mapped        sequencing reads at the spatially adjacent segment;    -   (d) building a hidden Markov model comprising:        -   (i) a plurality of hidden states comprising a copy number            for each of the spatially adjacent segments or a plurality            of sub-segments within each of the spatially adjacent            segments,        -   (ii) a plurality of observation states comprising the number            of sequencing reads mapped to each spatially adjacent            segment, and        -   (iii) the copy number likelihood model for each spatially            adjacent segment;    -   (e) parameterizing the hidden Markov model comprising adjusting        each copy number likelihood model to fit the determined number        of sequencing reads mapped to each spatially adjacent segment;        and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 3. The method of embodiment 1 or 2, further comprisingdetermining a most probable copy number of a section within the regionof interest, wherein the section comprises a plurality of spatiallyadjacent segments comprising the interrogated segment.

Embodiment 4. The method of any one of embodiments 1-3, wherein the copynumber likelihood model comprises a distribution for two or more copynumber states.

Embodiment 5. The method of any one of embodiments 1-4, wherein the copynumber likelihood model comprises a negative binomial distribution,wherein the negative binomial distribution is not a Poissondistribution.

Embodiment 6. The method of any one of embodiments 1-5, wherein theexpected number of sequencing reads is based on an average number ofmapped sequencing reads at a corresponding segment across a plurality ofsequencing libraries and an average number of mapped sequencing readsacross a plurality of segments of interest within the test sequencinglibrary, wherein the average number of mapped sequencing reads at acorresponding segment across a plurality of sequencing libraries or theaverage number of mapped sequencing reads across a plurality of segmentsof interest within the test sequencing library is a normalized average.

Embodiment 7. The method of any one of embodiments 1-6, wherein the copynumber likelihood model is adjusted to account for the presence of GCcontent bias.

Embodiment 8. The method of embodiment 6 or 7, wherein the adjustmentdepends on the GC content of the capture probe corresponding to theinterrogated segment or the GC content of the interrogated segment.

Embodiment 9. The method of any one of embodiments 1-8, wherein thehidden Markov model comprises a transition probability of the copynumber of the interrogated segment for a given copy number of aspatially adjacent segment.

Embodiment 10. The method of any one of embodiments 1-9, wherein thehidden Markov model comprises a plurality of transition probabilities ofthe copy number of a sub-segment in the plurality of sub-segments withinthe interrogated segment for a given copy number of a spatially adjacentsub-segment.

Embodiment 11. The method of embodiment 9 or 10, wherein the transitionprobability accounts for an average length of a copy number variant.

Embodiment 12. The method of any one of embodiments 9-11, wherein thetransition probability accounts for a prior probability of a copy numbervariant at the interrogated segment or a spatially adjacent segment.

Embodiment 13. The method of embodiment 11 or 12, wherein the averagelength of a copy number variant or the probability of a copy numbervariant at the interrogated segment are determined based on observationsin a human population.

Embodiment 14. The method of any one of embodiments 1-13, whereinparameterizing the hidden Markov model comprises accounting for one ormore spurious capture probes.

Embodiment 15. The method of embodiment 14, wherein accounting for oneor more spurious capture probes comprises weighting the one or moreobservation states in the plurality of observation states with aspurious capture probe indicator.

Embodiment 16. The method of embodiment 15, wherein the spurious captureprobe indicator is determined using a Bernoulli process.

Embodiment 17. The method of embodiment 15 or 16, wherein accounting forone or more of the capture probes being spurious comprises usingexpectation-maximization.

Embodiment 18. The method of any one of embodiments 14-17, wherein if acapture probe is determined to be spurious, the likelihood informationfrom that capture probe is disregarded in the copy number likelihoodmodel.

Embodiment 19. The method of any one of embodiments 1-18, wherein theparameterizing of the hidden Markov model comprises accounting for noisein the number of mapped sequencing reads.

Embodiment 20. The method of any one of embodiments 1-19, whereinaccounting for noise in the number of mapped sequencing reads comprisesadjusting the copy number likelihood model.

Embodiment 21. The method of embodiment 20, wherein adjusting the copynumber likelihood model to account for the noise comprises anexpectation-maximization step.

Embodiment 22. The method of embodiment 21 wherein theexpectation-maximization step comprises weighing a level of noise in thenumber of mapped sequencing reads from the test sequencing library.

Embodiment 23. The method of embodiment 22, wherein theexpectation-maximization step comprises using a Quasi-Newtonian solver.

Embodiment 24. The method of any one of embodiments 19-23, wherein themost probable copy number of the interrogated segment is not called ifthe noise in the number of mapped sequencing reads is above apredetermined threshold.

Embodiment 25. The method of any one of embodiments 1-24, whereinsequencing reads from overlapping capture probes are merged.

Embodiment 26. The method of any one of embodiments 1-25, wherein aViterbi algorithm, a Quasi-Newton solver, or a Markov chain Monte Carlois used to determine the most probable copy number of the interrogatedsegment.

Embodiment 27. The method of any one of embodiments 1-26, furthercomprising determining a confidence of the most probable copy number ofthe segment.

Embodiment 28. The method of any one of embodiments 1-27, wherein theregion of interest is a region within genomic DNA.

Embodiment 29. The method of any one of embodiments 1-28, wherein thetest sequencing library is derived from cell-free DNA.

Embodiment 30. The method of any one of embodiments 1-29, furthercomprising reporting the most probable copy number of the interrogatedsegment.

Embodiment 31. The method of any one of embodiments 1-29, furthercomprising reporting a copy number variant.

Embodiment 32. The method of embodiment 31, wherein the copy numbervariant is reported to a patient or a healthcare provider.

Embodiment 33. The method of any one of embodiments 1-32, furthercomprising providing a medical diagnosis based on the most probable copynumber of the interrogated segment.

Embodiment 34. The method of any one of embodiments 1-33, furthercomprising suggesting a treatment regimen based on the most probablecopy number of the interrogated segment.

Embodiment 35. A method for determining a copy number variantabnormality within a region of interest, comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to an interrogated segment within the        region of interest, wherein the test sequencing library is        enriched using one or more direct targeted sequencing capture        probes;    -   (b) determining a number of sequencing reads mapped to the        interrogated segment;    -   (c) determining a copy number likelihood model based on an        expected number of sequencing reads mapped to the interrogated        segment;    -   (d) building a hidden Markov model comprising:        -   (i) one or more hidden states comprising a copy number            corresponding to the interrogated segment or a plurality of            sub-segments within the interrogated segment,        -   (ii) an observation state comprising the number of            sequencing reads mapped to the interrogated segment; and        -   (iii) the copy number likelihood model;    -   (e) parameterizing the hidden Markov model by adjusting the copy        number likelihood model to fit the determined number of        sequencing reads mapped to the interrogated segment; and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model;    -   (g) determining a copy number variant abnormality based on the        most probable copy number of the interrogated segment.

Embodiment 36. A method for determining a copy number variantabnormality within a region of interest, comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to a plurality of spatially adjacent        segments, wherein the plurality of spatially adjacent segments        comprises an interrogated segment, and wherein the test        sequencing library is enriched using a plurality of spatially        adjacent direct targeted sequencing capture probes;    -   (b) determining a number of sequencing reads mapped to each        spatially adjacent segment;    -   (c) determining a copy number likelihood model for each        spatially adjacent segment based on an expected number of mapped        sequencing reads at the spatially adjacent segment;    -   (d) building a hidden Markov model comprising:        -   (i) a plurality of hidden states comprising a copy number            for each of the spatially adjacent segments or a plurality            of sub-segments within each of the spatially adjacent            segments,        -   (ii) a plurality of observation states comprising the number            of sequencing reads mapped to each spatially adjacent            segment, and        -   (iii) the copy number likelihood model for each spatially            adjacent segment;    -   (e) parameterizing the hidden Markov model comprising adjusting        each copy number likelihood model to fit the determined number        of sequencing reads mapped to each spatially adjacent segment;        and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model;    -   (g) determining a copy number variant abnormality based on the        most probable copy number of the interrogated segment.

Embodiment 37. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to a plurality of segments within a        region of interest, wherein the test sequencing library is        enriched using a plurality of capture probes, and wherein the        plurality of segments comprises the interrogated segment;    -   (b) determining a number of sequencing reads mapped to each        segment;    -   (c) determining a copy number likelihood model for the segment        based on an expected number of mapped sequencing reads at each        segment, wherein the expected number of mapped sequencing reads        is corrected for GC content of the segment; and    -   (d) determining a most probable copy number of the interrogated        segment based on the copy number likelihood model.

Embodiment 38. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to the interrogated segment, wherein the        test sequencing library is enriched using a plurality of capture        probes;    -   (b) determining a number of sequencing reads mapped to the        interrogated segment;    -   (c) determining a copy number likelihood model based on an        expected number of sequencing reads mapped to the interrogated        segment, wherein the expected number of mapped sequencing reads        is corrected for GC content of the interrogated segment;    -   (d) building a hidden Markov model comprising:        -   (i) one or more hidden states comprising a copy number            corresponding to the interrogated segment or a plurality of            sub-segments within the interrogated segment,        -   (ii) an observation state comprising the number of            sequencing reads mapped to the interrogated segment; and        -   (iii) the copy number likelihood model;    -   (e) parameterizing the hidden Markov model by adjusting the copy        number likelihood model to fit the determined number of        sequencing reads mapped to the interrogated segment; and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 39. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to a plurality of spatially adjacent        segments, wherein the plurality of spatially adjacent segments        comprises the interrogated segment, and wherein the test        sequencing library is enriched using a plurality of spatially        adjacent capture probes;    -   (b) determining a number of sequencing reads mapped to each        spatially adjacent segment;    -   (c) determining a copy number likelihood model for each        spatially adjacent segment based on an expected number of mapped        sequencing reads at the spatially adjacent segment, wherein the        expected number of mapped sequencing reads is corrected for GC        content of the spatially adjacent segment;    -   (d) building a hidden Markov model comprising:        -   (i) a plurality of hidden states comprising a copy number            for each of the spatially adjacent segments or a plurality            of sub-segments within each of the spatially adjacent            segments,        -   (ii) a plurality of observation states comprising the number            of sequencing reads mapped to each spatially adjacent            segment, and        -   (iii) the copy number likelihood model for each spatially            adjacent segment;    -   (e) parameterizing the hidden Markov model comprising adjusting        each copy number likelihood model to fit the determined number        of sequencing reads mapped to each spatially adjacent segment;        and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 40. The method of any one of embodiments 37-39, wherein thecapture probes are direct targeted sequencing capture probes.

Embodiment 41. The method of any one of embodiments 37-40, wherein thecapture probes enrich the sequencing library using hybrid capturetechniques.

Embodiment 42. The method of any one of embodiments 37-41, wherein theexpected number of sequencing reads is corrected for the GC content bymultiplying the expected number of sequencing reads at any given segmentby a GC bias correction factor for that segment, wherein the GC biascorrection factor is determined for the test sequencing library.

Embodiment 43. The method of embodiment 42, wherein the GC biascorrection factor is determined by:

-   -   fitting a second order function to a plurality of data points,        wherein the data points each comprises a normalized number of        sequencing reads mapped to a segment and the GC content of that        segment, and wherein the plurality of data points represent a        plurality of segments enriched by the capture probes in the test        sequencing library; and    -   defining the GC bias correction factor to be the normalized        number of sequencing reads determined by the second order        function for the GC content of the segment.

Embodiment 44. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to the interrogated segment, wherein the        test sequencing library is enriched using one or more capture        probes;    -   (b) determining a number of sequencing reads mapped to the        interrogated segment;    -   (c) determining a copy number likelihood model based on an        expected number of sequencing reads mapped to the interrogated        segment;    -   (d) building a hidden Markov model comprising:        -   (i) one or more hidden states comprising a copy number            corresponding to the interrogated segment or a plurality of            sub-segments within the interrogated segment,        -   (ii) an observation state comprising the number of            sequencing reads mapped to the interrogated segment; and        -   (iii) the copy number likelihood model;    -   (e) parameterizing the hidden Markov model by adjusting the copy        number likelihood model to fit the determined number of        sequencing reads mapped to the interrogated segment and        accounting for one or more spurious capture probes; and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 45. A method for determining a copy number of an interrogatedsegment within a region of interest comprising:

-   -   (a) mapping a plurality of sequencing reads generated from a        test sequencing library to a plurality of spatially adjacent        segments, wherein the plurality of spatially adjacent segments        comprises the interrogated segment, and wherein the test        sequencing library is enriched using a plurality of spatially        adjacent direct targeted sequencing capture probes;    -   (b) determining a number of sequencing reads mapped to each        spatially adjacent segment;    -   (c) determining a copy number likelihood model for each        spatially adjacent segment based on an expected number of mapped        sequencing reads at the spatially adjacent segment;    -   (d) building a hidden Markov model comprising:        -   (i) a plurality of hidden states comprising a copy number            for each of the spatially adjacent segments or a plurality            of sub-segments within each of the spatially adjacent            segments,        -   (ii) a plurality of observation states comprising the number            of sequencing reads mapped to each spatially adjacent            segment, and        -   (iii) the copy number likelihood model for each spatially            adjacent segment;    -   (e) parameterizing the hidden Markov model comprising adjusting        each copy number likelihood model to fit the determined number        of sequencing reads mapped to each spatially adjacent segment        and accounting for one or more spurious capture probes; and    -   (f) determining a most probable copy number of the interrogated        segment based on the parameterized hidden Markov model.

Embodiment 46. The method of embodiment 44 or 45, wherein accounting forone or more spurious capture probes comprises weighting the one or moreobservation states in the plurality of observation states with aspurious capture probe indicator.

Embodiment 47. The method of embodiment 46, wherein the spurious captureprobe indicator is determined using a Bernoulli process.

Embodiment 48. The method of embodiment 46 or 47, wherein accounting forone or more of the capture probes being spurious comprises usingexpectation-maximization.

Embodiment 49. The method of any one of embodiments 44-48, wherein themost probable copy number of the interrogated segment or the one or moresub-segments of the interrogated segment is not called if the captureprobe associated with the interrogated segment is determined to bespurious.

Embodiment 50. The method of any one of embodiments 44-48, wherein themost probable copy number of the interrogated segment or the one or moresub-segments of the interrogated segment is not called if theprobability of a capture probe being spurious is above a predeterminedthreshold.

Embodiment 51. The method of any one of embodiments 44-50, wherein thecapture probes are direct targeted sequencing capture probes.

Embodiment 52. The method of any one of embodiments 44-50, wherein thecapture probes enrich the sequencing library using hybrid capturetechniques.

Embodiment 53. The method of any one of embodiments 1-52, wherein theinterrogated segment is at least 100 bases in length.

Embodiment 54. A computer system comprising a computer-readable mediumcomprising instructions for carrying out the method of any one ofembodiments 1-53.

EXAMPLE

The following example illustrates using a hidden Markov model to callthe copy number state for segments within the BRCA1 and BRCA2 genes.Approximately 450 capture probes were used to enrich the BRCA gene from48 different sequencing libraries by direct targeted sequencing. Eachcapture probe corresponds to a segment within the gene. The firstnucleotide of each segment of interest corresponds to the firstnucleotide of the sequence that hybridizes to the capture probe mappedat the segment of interest. Enriched sequencing libraries were thensequenced using an Illumina HiSeq 2500 next generation sequencer.

Sequencing of the 48 test sequencing libraries generated multiplesequencing reads. Sequencing reads were mapped to the segments withinthe BRCA gene. Overlapping and correlated capture probes were merged tocorrespond to a single segment. Once it is accounted for merging oroverlapping probes, a number of mapped sequencing reads was determinedfor each segment within the region of interest.

The number of mapped sequencing reads was used to determine the mostprobable copy number state for each of the segments. First a copy numberlikelihood model was built comprising a negative binomial distribution(wherein the negative binomial distribution is not a Poissondistribution) for the expected number of sequencing reads for a copynumber state of 0, 1, 2, 3 and 4 for each of the segments for each ofthe 48 test sequencing libraries. The copy number likelihooddistributions in the model gave a probability that that the copy numberfor that distribution was correct given the observed number ofsequencing reads. The most probable copy number state for the majoritythe segments in each of the test sequencing libraries was 2.

Each segment was divided into sub-segments of 1 nucleotide each. Ahidden Markov model was built with a hidden state (a hidden copy number)for each sub-segment, an observation state (the determined number ofmapped sequencing reads) for each segment, and the copy numberlikelihood model to indicate the probability of the observed state giventhe hidden state. The hidden Markov model also included transitionprobabilities between spatially adjacent segments (that is, between thehidden states). The following stochastic transition matrix was used torepresent the transition probability of a copy number state of asubsequent spatially adjacent sub-segment given the copy number state ofa preceding spatially adjacent sub-segment.

${p\left( C_{i + 1} \middle| C_{i} \right)} = \begin{bmatrix}{1 - r_{01}} & r_{10} & 0 & 0 & 0 \\r_{01} & {1 - r_{12} - r_{10}} & r_{21} & 0 & 0 \\0 & r_{12} & {1 - r_{23} - r_{21}} & r_{32} & 0 \\0 & 0 & r_{23} & {1 - r_{32} - r_{34}} & r_{43} \\0 & 0 & 0 & r_{34} & {1 - r_{43}}\end{bmatrix}$

wherein C_(i) is the copy number state of a first sub-segment; C_(i+1)is the copy number state of the second sub-segment; and r_(ab)represents transition from a copy state of a to a copy state of b. Toset the transition, the average length of a copy number variant in humanpopulations and the probability of observing a copy number variant inhuman populations were taken into account. Specifically the transitionswere set based on the following formulas:

${r_{01} = {r_{12} = {r_{32} = {r_{43} = \frac{1}{\left\langle l \right\rangle_{CNV}}}}}}{r_{21} = {r_{12}\frac{p_{CNV}}{1 - {2p_{CNV}} - {2p_{CNV}^{2}}}}}$

wherein <l>_(CNV) denotes the length of a copy number variant and wasset to 6200 nucleotides; and wherein P_(CNV) denotes the probability ofa copy number variant which was set to 0.001.The probability of the copynumber variant was set by balancing the thresholds for confident callingand retesting of calls to achieve the desired sensitivity andspecificity, but the prior is set irrespective of the validation.Subsequently the threshold can be tuned based on the frequency of a copynumber call within the region.

The hidden Markov model was parameterized to adjust the copy numberlikelihood model (which accounted for GC content bias), as well as toaccount for spurious capture probes and noise within the test sequencinglibraries. Optimization was done using Expectation-Maximizationalgorithms. The Baum-Welch was used for the Expectation step and theQuasi-Newton was used for the Maximization step. A Viterbi algorithm wasused to determine the most probable copy number at each segment.

While the copy number (i.e., the hidden state) was determined for eachnucleotide within the BRCA gene, the most likely copy number call wasmade for each segment. This allows the model to discriminate and discardvery small insertion or deletion that would not constitute a copy numbervariant. FIG. 7 shows the copy number state for a portion of thespatially adjacent segments within the BRCA gene across all testsequencing libraries without using the parameterized hidden Markov model(that is, using the copy number likelihood model alone). FIG. 8 showsthe most likely copy number after parameterizing the hidden Markov modeland determining a most probable copy number of the segments based on theparameterized hidden Markov model.

What is claimed is:
 1. A system for determining a copy number of aninterrogated segment of nucleic acids within a region of interest of agenome, the system comprising one or more processors operable to: (a)map a plurality of sequencing reads of nucleic acids generated from atest sequencing library to the interrogated segment; (b) determine anumber of sequencing reads mapped to the interrogated segment; (c)determine a copy number likelihood model using a plurality of likelihooddistributions associated with an expected number of sequencing readsmapped to the interrogated segment; (d) build a hidden Markov modelcomprising: (i) one or more hidden states comprising a copy numbercorresponding to the interrogated segment or a plurality of sub-segmentswithin the interrogated segment, (ii) an observation state comprisingthe number of sequencing reads mapped to the interrogated segment; and(iii) the copy number likelihood model; (e) parameterize the hiddenMarkov model by adjusting the copy number likelihood model to fit thedetermined number of sequencing reads mapped to the interrogated segmentby allowing portions of the likelihood distributions to float; and (f)determine a most probable copy number of the interrogated segment byoptimizing the parameterized hidden Markov model.
 2. The system of claim1, wherein the one or more processors are further operable to: map theplurality of sequencing reads generated from the test sequencing libraryto a plurality of spatially adjacent segments, wherein the plurality ofspatially adjacent segments comprises the interrogated segment;determine a number of sequencing reads mapped to each spatially adjacentsegment; determine a copy number likelihood model for each spatiallyadjacent segment using a plurality of likelihood distributionsassociated with an expected number of mapped sequencing reads at thespatially adjacent segment; build the hidden Markov model, wherein thehidden Markov model comprises comprising: (i) a plurality of hiddenstates comprising a copy number for each of the spatially adjacentsegments or a plurality of sub-segments within each of the spatiallyadjacent segments, (ii) a plurality of observation states comprising thenumber of sequencing reads mapped to each spatially adjacent segment,and (iii) the copy number likelihood model for each spatially adjacentsegment; and parameterize the hidden Markov model comprising adjustingeach copy number likelihood model to fit the determined number ofsequencing reads mapped to each spatially adjacent segment by allowingportions of the likelihood distributions to float.
 3. The system ofclaim 1, wherein the one or more processors are further operable todetermine a most probable copy number of a section within the region ofinterest, wherein the section comprises a plurality of spatiallyadjacent segments comprising the interrogated segment.
 4. The system ofclaim 1, wherein the copy number likelihood model comprises adistribution for two or more copy number states or a negative binomialdistribution, wherein the negative binomial distribution is not aPoisson distribution.
 5. The system of claim 1, wherein the expectednumber of sequencing reads is based on an average number of mappedsequencing reads at a corresponding segment across a plurality ofsequencing libraries and an average number of mapped sequencing readsacross a plurality of segments of interest within the test sequencinglibrary, wherein the average number of mapped sequencing reads at acorresponding segment across a plurality of sequencing libraries or theaverage number of mapped sequencing reads across a plurality of segmentsof interest within the test sequencing library is a normalized average.6. The system of claim 1, wherein the copy number likelihood model isadjusted to account for the presence of GC content bias, and whereinadjustment of the copy number likelihood model depends on the GC contentof the capture probe corresponding to the interrogated segment or the GCcontent of the interrogated segment.
 7. The system of claim 1, whereinthe hidden Markov model comprises a plurality of transitionprobabilities of the copy number of a sub-segment in the plurality ofsub-segments within the interrogated segment for a given copy number ofa spatially adjacent sub-segment.
 8. The system of claim 1, wherein thehidden Markov model comprises a transition probability of the copynumber of the interrogated segment for a given copy number of aspatially adjacent segment, wherein the transition probability accountsfor an average length of a copy number variant or for a priorprobability of a copy number variant at the interrogated segment or aspatially adjacent segment, wherein the average length of a copy numbervariant or the probability of a copy number variant at the interrogatedsegment are determined based on observations in a human population.. 9.The system of claim 1, wherein the one or more processors are furtheroperable to parameterize the hidden Markov model by accounting for oneor more spurious capture probes, wherein accounting for one or morespurious capture probes comprises weighting the one or more observationstates in the plurality of observation states with a spurious captureprobe indicator or optimizing the parameterized hidden Markov modelusing an expectation-maximization step, wherein the spurious captureprobe indicator comprises a Bernoulli distribution of a priorobservation state in the hidden Markov model, and if a capture probe isdetermined to be spurious, the likelihood information from that captureprobe is disregarded in the copy number likelihood model.
 10. The systemof claim 1, wherein the one or more processors are further operable toparameterize the hidden Markov model by accounting for noise in thenumber of mapped sequencing reads, wherein accounting for noise in thenumber of mapped sequencing reads comprises adjusting the copy numberlikelihood model by adjusting a dispersion of a copy number likelihooddistribution in the copy number likelihood model, wherein adjusting thecopy number likelihood model to account for the noise comprisesadjusting the dispersion of the copy number likelihood distribution inthe copy number likelihood model via an expectation-maximization step,wherein the expectation-maximization step comprises weighing a level ofnoise in the number of mapped sequencing reads from the test sequencinglibrary, wherein the expectation-maximization step comprises using aQuasi-Newtonian solver, and wherein the most probable copy number of theinterrogated segment is not called if the noise in the number of mappedsequencing reads is above a predetermined threshold.
 11. The system ofclaim 1, wherein sequencing reads from overlapping capture probes aremerged.
 12. The system of claim 1, wherein the one or more processorsare further operable to implement a Viterbi algorithm to determine themost probable copy number of the interrogated segment.
 13. The system ofclaim 1, wherein the one or more processors are further operable todetermine a confidence of the most probable copy number of the segment.